Quiz

Exponents and Surds

Surds

Home

About

Subjects

Contact

Life After Matric

Coursemaccon Academy

is a Subsidiary of

Coursemaccon Business Solutions

Quiz

Surds Score: 0/10

1. Which of the following is a Surd?

\sqrt[]{-5}

\sqrt[]{100}

\sqrt[3]{27}

D. None of the above

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer:

$\sqrt[]{8}$

A. 4

\sqrt[3]{2}

C. 2

\sqrt[]{2}

D. None of the above.

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer:

$\sqrt[]{15}$ x $\sqrt[]{5}$

A. 2

\sqrt[]{5}

B. 5

\sqrt[]{3}

C. 5

D. None of the above.

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer:

$\sqrt[]{9}$ - $\sqrt[]{4}$

\sqrt[]{5}

B. 1

C. 6

D. None of the above.

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer:

$\sqrt[]{a 2 - b 2}$

A. 2a + 2b

B. 0

C. a - b

D. None of the above

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer:

$\frac{\sqrt[]{48}}{\sqrt[]{3}}$

A. 3

\sqrt[]{3}

B. 2

C. 4

D. None of the above

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$

7. Simplify and choose the correct answer:

$\frac{9 + \sqrt[]{45}}{3}$

A. 9 +

\sqrt[]{5}

B. 12 +

\sqrt[]{45}

C. 3 +

\sqrt[]{5}

D. None of the above

8. Simplify and choose the correct answer: $\frac{5}{4 + \sqrt[]{11}}$

8. Simplify and choose the correct answer:

$\frac{5}{4 + \sqrt[]{11}}$

A. 4 -

\sqrt[]{11}

B. 4 +

\sqrt[]{11}

C. 5

D. None of the above

9. Simplify and choose the correct answer: $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

9. Simplify and choose the correct answer:

$\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

A. 2

\sqrt[]{8}

\sqrt[]{5}

\sqrt[]{3}

\sqrt[]{5}

\sqrt[]{3}

D. None of the above

10. Simplify and choose the correct answer: $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

10. Simplify and choose the correct answer:

$\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

A. 1

B. 8 + 2

\sqrt[]{15}

C. 4 +

\sqrt[]{15}

D. None of the above

What does HTML stand for?

Quiz Results

Your score is 0 out of 10

Solutions

Surds Question 1 of 10

1. Which of the following is a Surd?

\sqrt[]{-5}

\sqrt[]{100}

\sqrt[3]{27}

D. None of the above

Correct Answer
Option D

Detailed Solution

Solution Details

Surds

All n-th roots that are not equal to a Rational Number are called Surds.

This means if we express them as decimals, we get non-recurring or non-terminating decimals.

For more info please see

Surds

Surds

All n-th roots that are not equal to a Rational Number are called Surds.

This means if we express them as decimals, we get non-recurring or non-terminating decimals.

For more info please see

Surds

Surds

All n-th roots that are not equal to a Rational Number are called Surds.

This means if we express them as decimals, we get non-recurring or non-terminating decimals.

For more info please see

Surds

Surds Question 2 of 10

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer:

$\sqrt[]{8}$

A. 4

\sqrt[3]{2}

C. 2

\sqrt[]{2}

D. None of the above.

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\sqrt[]{8}$

• $\sqrt[]{8}$ = $\sqrt[]{4 x 2}$ = $\sqrt[]{4}$ x $\sqrt[]{2}$ = 2 $\sqrt[]{2}$

For more info please see

Surds

Given $\sqrt[]{8}$

• $\sqrt[]{8}$ = $\sqrt[]{4 x 2}$ = $\sqrt[]{4}$ x $\sqrt[]{2}$ = 2 $\sqrt[]{2}$

For more info please see

Surds

Given $\sqrt[]{8}$

• $\sqrt[]{8}$

= $\sqrt[]{4 x 2}$

= $\sqrt[]{4}$ x $\sqrt[]{2}$

= 2 $\sqrt[]{2}$

For more info please see

Surds

Surds Question 3 of 10

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer:

$\sqrt[]{15}$ x $\sqrt[]{5}$

A. 2

\sqrt[]{5}

B. 5

\sqrt[]{3}

C. 5

D. None of the above.

Correct Answer
Option B

Detailed Solution

Solution Details

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$ = $\sqrt[]{15 x 5}$ = $\sqrt[]{75}$ = $\sqrt[]{25 x 3}$ = $\sqrt[]{25}$ x $\sqrt[]{3}$ = 5 $\sqrt[]{3}$

For more info please see

Surds

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$ = $\sqrt[]{15 x 5}$ = $\sqrt[]{75}$ = $\sqrt[]{25 x 3}$ = $\sqrt[]{25}$ x $\sqrt[]{3}$ = 5 $\sqrt[]{3}$

For more info please see

Surds

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$

= $\sqrt[]{15 x 5}$

= $\sqrt[]{75}$

= $\sqrt[]{25 x 3}$

= $\sqrt[]{25}$ x $\sqrt[]{3}$

= 5 $\sqrt[]{3}$

For more info please see

Surds

Surds Question 4 of 10

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer:

$\sqrt[]{9}$ - $\sqrt[]{4}$

\sqrt[]{5}

B. 1

C. 6

D. None of the above.

Correct Answer
Option B

Detailed Solution

Solution Details

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$ = 3 - 2 = 1

For more info please see

Surds

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$ = 3 - 2 = 1

For more info please see

Surds

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$

= 3 - 2

= 1

For more info please see

Surds

Surds Question 5 of 10

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer:

$\sqrt[]{a 2 - b 2}$

A. 2a + 2b

B. 0

C. a - b

D. None of the above

Correct Answer
Option D

Detailed Solution

Solution Details

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

For more info please see

Surds

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

For more info please see

Surds

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

For more info please see

Surds

Surds Question 6 of 10

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer:

$\frac{\sqrt[]{48}}{\sqrt[]{3}}$

A. 3

\sqrt[]{3}

B. 2

C. 4

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$ = $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$ = 4

For more info please see

Surds

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$ = $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$ = 4

For more info please see

Surds

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

= $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$

= $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$

= $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$

= 4

For more info please see

Surds

Surds Question 7 of 10

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$

7. Simplify and choose the correct answer:

$\frac{9 + \sqrt[]{45}}{3}$

A. 9 +

\sqrt[]{5}

B. 12 +

\sqrt[]{45}

C. 3 +

\sqrt[]{5}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{9 + \sqrt[]{45}}{3}$

• $\frac{9 + \sqrt[]{45}}{3}$ = $\frac{9 + \sqrt[]{9 x 5}}{3}$ = $\frac{9 + \sqrt[]{9} x \sqrt[]{5}}{3}$ = $\frac{9 + 3 x \sqrt[]{5}}{3}$ = $\frac{3 ( 3 + \sqrt[]{5})}{3}$ = 3 + $\sqrt[]{5}$

For more info please see

Surds

Given $\frac{9 + \sqrt[]{45}}{3}$

• $\frac{9 + \sqrt[]{45}}{3}$ = $\frac{9 + \sqrt[]{9 x 5}}{3}$ = $\frac{9 + \sqrt[]{9} x \sqrt[]{5}}{3}$ = $\frac{9 + 3 x \sqrt[]{5}}{3}$

= $\frac{3 ( 3 + \sqrt[]{5})}{3}$ = 3 + $\sqrt[]{5}$

For more info please see

Surds

Given $\frac{9 + \sqrt[]{45}}{3}$

• $\frac{9 + \sqrt[]{45}}{3}$

= $\frac{9 + \sqrt[]{9 x 5}}{3}$

= $\frac{9 + \sqrt[]{9} x \sqrt[]{5}}{3}$

= $\frac{9 + 3 x \sqrt[]{5}}{3}$

= $\frac{3 ( 3 + \sqrt[]{5})}{3}$

= 3 + $\sqrt[]{5}$

For more info please see

Surds

Surds Question 8 of 10

8. Simplify and choose the correct answer: $\frac{5}{4 + \sqrt[]{11}}$

8. Simplify and choose the correct answer:

$\frac{5}{4 + \sqrt[]{11}}$

A. 4 -

\sqrt[]{11}

B. 4 +

\sqrt[]{11}

C. 5

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given $\frac{5}{4 + \sqrt[]{11}}$

• $\frac{5}{4 + \sqrt[]{11}}$ = $\frac{5}{4 + \sqrt[]{11}}$ x $\frac{4 - \sqrt[]{11}}{4 - \sqrt[]{11}}$ = $\frac{5 ( 4 - \sqrt[]{11})}{( 4 + \sqrt[]{11})( 4 - \sqrt[]{11})}$ = $\frac{5 ( 4 - \sqrt[]{11})}{16 - 11}$ = $\frac{5 ( 4 - \sqrt[]{11})}{5}$ = 4 - $\sqrt[]{11}$

For more info please see

Surds

Given $\frac{5}{4 + \sqrt[]{11}}$

• $\frac{5}{4 + \sqrt[]{11}}$ = $\frac{5}{4 + \sqrt[]{11}}$ x $\frac{4 - \sqrt[]{11}}{4 - \sqrt[]{11}}$ = $\frac{5 ( 4 - \sqrt[]{11})}{( 4 + \sqrt[]{11})( 4 - \sqrt[]{11})}$

= $\frac{5 ( 4 - \sqrt[]{11})}{16 - 11}$ = $\frac{5 ( 4 - \sqrt[]{11})}{5}$ = 4 - $\sqrt[]{11}$

For more info please see

Surds

Given $\frac{5}{4 + \sqrt[]{11}}$

• $\frac{5}{4 + \sqrt[]{11}}$

= $\frac{5}{4 + \sqrt[]{11}}$ x $\frac{4 - \sqrt[]{11}}{4 - \sqrt[]{11}}$

= $\frac{5 ( 4 - \sqrt[]{11})}{( 4 + \sqrt[]{11})( 4 - \sqrt[]{11})}$

= $\frac{5 ( 4 - \sqrt[]{11})}{16 - 11}$

= $\frac{5 ( 4 - \sqrt[]{11})}{5}$

= 4 - $\sqrt[]{11}$

For more info please see

Surds

Surds Question 9 of 10

9. Simplify and choose the correct answer: $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

9. Simplify and choose the correct answer:

$\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

A. 2

\sqrt[]{8}

\sqrt[]{5}

\sqrt[]{3}

\sqrt[]{5}

\sqrt[]{3}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$ = $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$ = $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$ = $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{5 - 3}$ = $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{2}$ = $\sqrt[]{5}$ + $\sqrt[]{3}$

For more info please see

Surds

Given $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$ = $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$ = $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$

= $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{5 - 3}$ = $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{2}$ = $\sqrt[]{5}$ + $\sqrt[]{3}$

For more info please see

Surds

Given $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

= $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$

= $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$

= $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{5 - 3}$

= $\frac{2 (\sqrt[]{5} + \sqrt[]{3})}{2}$

= $\sqrt[]{5}$ + $\sqrt[]{3}$

For more info please see

Surds

Surds Question 10 of 10

10. Simplify and choose the correct answer: $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

10. Simplify and choose the correct answer:

$\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

A. 1

B. 8 + 2

\sqrt[]{15}

C. 4 +

\sqrt[]{15}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$ = $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$ = $\frac{(\sqrt[]{5} + \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$ = $\frac{5 + 2 \sqrt[]{5 x 3} + 3}{5 - 3}$ = $\frac{8 + 2 \sqrt[]{15}}{2}$ = $\frac{2 ( 4 + \sqrt[]{15})}{2}$ = 4 + $\sqrt[]{15}$

For more info please see

Surds

Given $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$ = $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$ = $\frac{(\sqrt[]{5} + \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$

= $\frac{5 + 2 \sqrt[]{5 x 3} + 3}{5 - 3}$ = $\frac{8 + 2 \sqrt[]{15}}{2}$ = $\frac{2 ( 4 + \sqrt[]{15})}{2}$ = 4 + $\sqrt[]{15}$

For more info please see

Surds

Given $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

• $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

= $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$ x $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} + \sqrt[]{3}}$

= $\frac{(\sqrt[]{5} + \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}{(\sqrt[]{5} - \sqrt[]{3}) (\sqrt[]{5} + \sqrt[]{3})}$

= $\frac{5 + 2 \sqrt[]{5 x 3} + 3}{5 - 3}$

= $\frac{8 + 2 \sqrt[]{15}}{2}$

= $\frac{2 ( 4 + \sqrt[]{15})}{2}$

= 4 + $\sqrt[]{15}$

For more info please see

Surds

Quiz

Exponents and Surds

Surds

Quiz Quidelines

Quiz

1. Which of the following is a Surd?

1. Which of the following is a Surd?

1. Which of the following is a Surd?

2. Simplify and choose the correct answer: 8

2. Simplify and choose the correct answer: 8

2. Simplify and choose the correct answer: 8

3. Simplify and choose the correct answer: 15 x 5

3. Simplify and choose the correct answer: 15 x 5

3. Simplify and choose the correct answer: 15 x 5

4. Simplify and choose the correct answer: 9 - 4

4. Simplify and choose the correct answer: 9 - 4

4. Simplify and choose the correct answer: 9 - 4

5. Simplify and choose the correct answer: a2 - b2

5. Simplify and choose the correct answer: a2 - b2

5. Simplify and choose the correct answer: a2 - b2

6. Simplify and choose the correct answer: 48 3

6. Simplify and choose the correct answer: 48 3

6. Simplify and choose the correct answer: 48 3

7. Simplify and choose the correct answer: 9 + 45 3

7. Simplify and choose the correct answer: 9 + 45 3

7. Simplify and choose the correct answer: 9 + 45 3

8. Simplify and choose the correct answer: 5 4 + 11

8. Simplify and choose the correct answer: 5 4 + 11

8. Simplify and choose the correct answer: 5 4 + 11

9. Simplify and choose the correct answer: 2 5 - 3

9. Simplify and choose the correct answer: 2 5 - 3

9. Simplify and choose the correct answer: 2 5 - 3

10. Simplify and choose the correct answer: 5 + 3 5 - 3

10. Simplify and choose the correct answer: 5 + 3 5 - 3

10. Simplify and choose the correct answer: 5 + 3 5 - 3

What does HTML stand for?

Quiz Results

Solutions

1. Which of the following is a Surd?

1. Which of the following is a Surd?

1. Which of the following is a Surd?

Correct Answer Option D

Detailed Solution

Solution Details

Surds

Surds

Surds

2. Simplify and choose the correct answer: 8

2. Simplify and choose the correct answer: 8

2. Simplify and choose the correct answer: 8

Correct Answer Option C

Detailed Solution

Solution Details

Given 8

• 8 = 4 x 2 = 4 x 2 = 2 2

Given 8

• 8 = 4 x 2 = 4 x 2 = 2 2

Given 8

• 8 = 4 x 2 = 4 x 2 = 2 2

3. Simplify and choose the correct answer: 15 x 5

3. Simplify and choose the correct answer: 15 x 5

3. Simplify and choose the correct answer: 15 x 5

Correct Answer Option B

Detailed Solution

Solution Details

Given 15 x 5

• 15 x 5 = 15 x 5 = 75 = 25 x 3 = 25 x 3 = 5 3

Given 15 x 5

• 15 x 5 = 15 x 5 = 75 = 25 x 3 = 25 x 3 = 5 3

Given 15 x 5

• 15 x 5 = 15 x 5 = 75 = 25 x 3 = 25 x 3 = 5 3

4. Simplify and choose the correct answer: 9 - 4

4. Simplify and choose the correct answer: 9 - 4

4. Simplify and choose the correct answer: 9 - 4

Correct Answer Option B

Detailed Solution

Solution Details

Given 9 - 4

• 9 - 4 = 3 - 2 = 1

Given 9 - 4

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer:

$\sqrt[]{8}$

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer:

$\sqrt[]{15}$ x $\sqrt[]{5}$

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer:

$\sqrt[]{9}$ - $\sqrt[]{4}$

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer:

$\sqrt[]{a 2 - b 2}$

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer:

$\frac{\sqrt[]{48}}{\sqrt[]{3}}$

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$

7. Simplify and choose the correct answer:

$\frac{9 + \sqrt[]{45}}{3}$

8. Simplify and choose the correct answer: $\frac{5}{4 + \sqrt[]{11}}$

8. Simplify and choose the correct answer: $\frac{5}{4 + \sqrt[]{11}}$

8. Simplify and choose the correct answer:

$\frac{5}{4 + \sqrt[]{11}}$

9. Simplify and choose the correct answer: $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

9. Simplify and choose the correct answer: $\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

9. Simplify and choose the correct answer:

$\frac{2}{\sqrt[]{5} - \sqrt[]{3}}$

10. Simplify and choose the correct answer: $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

10. Simplify and choose the correct answer: $\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

10. Simplify and choose the correct answer:

$\frac{\sqrt[]{5} + \sqrt[]{3}}{\sqrt[]{5} - \sqrt[]{3}}$

Correct Answer
Option D

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer: $\sqrt[]{8}$

2. Simplify and choose the correct answer:

$\sqrt[]{8}$

Correct Answer
Option C

Given $\sqrt[]{8}$

• $\sqrt[]{8}$ = $\sqrt[]{4 x 2}$ = $\sqrt[]{4}$ x $\sqrt[]{2}$ = 2 $\sqrt[]{2}$

Given $\sqrt[]{8}$

• $\sqrt[]{8}$ = $\sqrt[]{4 x 2}$ = $\sqrt[]{4}$ x $\sqrt[]{2}$ = 2 $\sqrt[]{2}$

Given $\sqrt[]{8}$

• $\sqrt[]{8}$

= $\sqrt[]{4 x 2}$

= $\sqrt[]{4}$ x $\sqrt[]{2}$

= 2 $\sqrt[]{2}$

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer: $\sqrt[]{15}$ x $\sqrt[]{5}$

3. Simplify and choose the correct answer:

$\sqrt[]{15}$ x $\sqrt[]{5}$

Correct Answer
Option B

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$ = $\sqrt[]{15 x 5}$ = $\sqrt[]{75}$ = $\sqrt[]{25 x 3}$ = $\sqrt[]{25}$ x $\sqrt[]{3}$ = 5 $\sqrt[]{3}$

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$ = $\sqrt[]{15 x 5}$ = $\sqrt[]{75}$ = $\sqrt[]{25 x 3}$ = $\sqrt[]{25}$ x $\sqrt[]{3}$ = 5 $\sqrt[]{3}$

Given $\sqrt[]{15}$ x $\sqrt[]{5}$

• $\sqrt[]{15}$ x $\sqrt[]{5}$

= $\sqrt[]{15 x 5}$

= $\sqrt[]{75}$

= $\sqrt[]{25 x 3}$

= $\sqrt[]{25}$ x $\sqrt[]{3}$

= 5 $\sqrt[]{3}$

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer: $\sqrt[]{9}$ - $\sqrt[]{4}$

4. Simplify and choose the correct answer:

$\sqrt[]{9}$ - $\sqrt[]{4}$

Correct Answer
Option B

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$ = 3 - 2 = 1

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$ = 3 - 2 = 1

Given $\sqrt[]{9}$ - $\sqrt[]{4}$

• $\sqrt[]{9}$ - $\sqrt[]{4}$

= 3 - 2

= 1

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer: $\sqrt[]{a 2 - b 2}$

5. Simplify and choose the correct answer:

$\sqrt[]{a 2 - b 2}$

Correct Answer
Option D

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

Given $\sqrt[]{a 2 - b 2}$

• $\sqrt[]{a 2 - b 2}$ cannot be simplified.

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer: $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

6. Simplify and choose the correct answer:

$\frac{\sqrt[]{48}}{\sqrt[]{3}}$

Correct Answer
Option C

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$ = $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$ = 4

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$ = $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$ = $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$ = 4

Given $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

• $\frac{\sqrt[]{48}}{\sqrt[]{3}}$

= $\frac{\sqrt[]{16 x 3}}{\sqrt[]{3}}$

= $\frac{\sqrt[]{16} x \sqrt[]{3}}{\sqrt[]{3}}$

= $\frac{4 x \sqrt[]{3}}{\sqrt[]{3}}$

= 4

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$

7. Simplify and choose the correct answer: $\frac{9 + \sqrt[]{45}}{3}$