# Worksheet: Operations with Square Roots

In this worksheet, we will practice solving problems on the operations of the square roots and finding the conjugates of radical expressions and their product.

Q1:

Express in its simplest form.

• A
• B
• C
• D
• E

Q2:

Simplify by combining similar terms.

• A
• B
• C
• D
• E

Q3:

Expand .

• A
• B 55
• C
• D

Q4:

Express in its simplest form.

• A
• B
• C
• D
• E

Q5:

Express in its simplest form.

• A
• B
• C
• D

Q6:

Calculate .

• A
• B
• C
• D
• E

Q7:

Express in its simplest form.

• A
• B
• C
• D
• E

Q8:

Simplify .

• A
• B
• C
• D
• E

Q9:

Calculate .

Q10:

Calculate .

• A
• B
• C
• D
• E

Q11:

Given that , find the value of .

• A
• B
• C102
• D
• E70

Q12:

Simplify .

• A
• B
• C
• D
• E

Q13:

Given that and , find .

Q14:

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

• A
• B
• C
• D
• E

Q15:

What is the conjugate of ? Find the product of and its conjugate.

• A
• B
• C
• D
• E

Q16:

What is the conjugate of ? What is the product of and its conjugate?

• A
• B
• C
• D
• E

Q17:

Given that , find the value of .

• A 8 or 4
• B 0 or 4
• C 2 or 8
• D 0 or 8

Q18:

Simplify .

• A
• B
• C
• D3

Q19:

Express in its simplest form.

• A
• B
• C
• D
• E

Q20:

Given that , evaluate .

Q21:

Given that and , find .

• A
• B
• C
• D

Q22:

Given that and , find .

• A1
• B
• C
• D

Q23:

Calculate .

• A
• B
• C
• D
• E

Q24:

Calculate .

• A
• B
• C
• D

Q25:

Calculate .