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

Q1:

Given that , simplify .

• A
• B0
• C
• D

Q2:

Simplify .

• A
• B
• C
• D
• E

Q3:

Given that and , find the value of .

Q4:

Calculate .

Q5:

If and , is it true that ?

• Ano
• Byes

Q6:

Simplify .

• A
• B
• C
• D

Q7:

Given that , , and , find the value of .

• A
• B
• C
• D

Q8:

Given that and , find the value of .

• A
• B
• C
• D1
• E7

Q9:

Calculate .

• A
• B
• C
• D

Q10:

What is the value of ?

• A1
• B2
• C10
• D

Q11:

Find the value of .

Q12:

Express in the form where and are integers and takes the least possible value.

• A
• B
• C
• D

Q13:

Express in the form where and are integers and takes the least possible value.

• A
• B
• C
• D

Q14:

What is the value of ?

• A1
• B
• C
• D
• E

Q15:

Given that , simplify .

• A
• B
• C
• D
• E

Q16:

Simplify .

• A
• B
• C
• D
• E

Q17:

Simplify .

• A
• B
• C54
• D

Q18:

Solve .

• A
• B
• C
• D
• E

Q19:

Express in the form where and are integers and takes the least possible value.

• A
• B
• C
• D
• E

Q20:

Find the conjugate of , then find the product of and its conjugate.

• A, 249
• B, 249
• C, 1
• D, 126
• E, 255

Q21:

Calculate .

Q22:

What is the value of ?

• A
• B
• C
• D

Q23:

Which of the following is equal to ?

• A
• B
• C
• D
• E

Q24:

What is the value of ?

• A
• B
• C8
• D

Q25:

Is the cube root of a negative number positive or negative?

• Apositive
• Bnegative