# Worksheet: Rationalizing Denominators of Radicals

In this worksheet, we will practice rationalizing denominators of radicals.

Q1:

• A28
• B56
• C
• D8
• E

Q2:

Simplify by rationalizing the denominator.

• A
• B
• C
• D

Q3:

Simplify .

• A
• B
• C
• D

Q4:

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

Q5:

What is the conjugate of ? Express your answer in simplest form.

• A
• B
• C
• D
• E

Q6:

Given that and , find the value of .

• A
• B
• C
• D

Q7:

Given that and , find the value of .

• A
• B
• C
• D
• E

Q8:

Given that and , express in terms of .

• A
• B
• C
• D
• E

Q9:

Simplify .

• A
• B
• C
• D78

Q10:

• A
• B
• C
• D
• E

Q11:

Express in its simplest form.

• A
• B
• C
• D
• E

Q12:

Simplify by rationalizing the denominator.

• A
• B
• C
• D

Q13:

Simplify by rationalizing the denominator.

• A
• B
• C
• D

Q14:

• A20
• B60
• C
• D12
• E

Q15:

Given that , find the values of and .

• A,
• B,
• C,
• D,

Q16:

Given that , find the values of and .

• A,
• B,
• C,
• D,

Q17:

Given that , find the values of and .

• A,
• B,
• C,
• D,

Q18:

Simplify by rationalizing the denominator.

• A
• B
• C
• D

Q19:

Simplify by rationalizing the denominator.

• A
• B
• C
• D
• E

Q20:

Simplify by rationalizing the denominator.

• A
• B
• C
• D
• E

Q21:

• A28
• B56
• C8
• D

Q22:

Simplify by rationalizing the denominator.

• A
• B
• C
• D
• E

Q23:

Express in its simplest form.

• A
• B
• C
• D
• E

Q24:

Express in its simplest form.

• A
• B
• C
• D

Q25:

Given that and , find .