# Worksheet: Operations with Radicals

In this worksheet, we will practice performing mathematical operations on radicals and utilizing the conjugate to rationalize the denominator of a radical.

Q1:

Express in its simplest form.

• A
• B3
• C
• D

Q2:

Express in its simplest form.

• A
• B
• C
• D

Q3:

Given that and , determine the value of expressing your answer in simplest form.

• A
• B
• C
• D

Q4:

Express in its simplest form.

• A
• B
• C
• D

Q5:

Given that and , find the value of .

• A 16
• B 69
• C
• D

Q6:

Simplify .

• A
• B
• C
• D
• E4

Q7:

Given that and , find .

Q8:

Express in its simplest form.

• A
• B
• C
• D
• E

Q9:

Given that and , find expressing your answer in simplest form.

• A
• B
• C
• D
• E

Q10:

Express in its simplest form.

• A
• B
• C 15
• D

Q11:

What is the value of ?

Q12:

Given that and , find .

Q13:

Given that and , find expressing your answer in simplest form.

• A
• B
• C
• D
• E

Q14:

Given that and , find expressing your answer in simplest form.

• A 7
• B
• C 5
• D
• E

Q15:

Given that and , find .

Q16:

Given that and , find the value of .

• A
• B
• C
• D
• E

Q17:

Given that and , find the value of .

• A
• B
• C 0
• D
• E

Q18:

Given that and , find the value of .

Q19:

Calculate .

• A
• B
• C
• D
• E

Q20:

Express in its simplest form.

• A
• B
• C
• D

Q21:

Evaluate .

Q22:

Determine the value of .

• A
• B
• C
• D
• E

Q23:

Express in its simplest form.

• A
• B
• C
• D
• E

Q24:

Find the value of .

• A
• B
• C
• D0

Q25:

Given that and , find the value of .