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 1 2 8 + 1 8 8 1 2 in its simplest form.

  • A 7 6
  • B 3 2
  • C 2
  • D 7 2
  • E 1 5 2

Q2:

Simplify 5 × 5 by combining similar terms.

  • A 5
  • B 2
  • C ( 2 )
  • D 5
  • E 2 5

Q3:

Expand 6 7 .

  • A 5 5 + 1 4 6
  • B 55
  • C 5 5 7 6
  • D 5 5 1 4 6

Q4:

Express 9 𝑥 1 0 0 𝑦 𝑧 in its simplest form.

  • A | | | 9 𝑥 1 0 0 𝑦 𝑧 | | |
  • B 3 𝑥 1 0 𝑦 𝑧
  • C 3 𝑥 1 0 0 𝑦 𝑧
  • D | | | 3 𝑥 1 0 𝑦 𝑧 | | |
  • E 3 𝑥 1 0 𝑦 𝑧

Q5:

Express 3 + 1 2 7 5 in its simplest form.

  • A 6 0
  • B 2 0 3
  • C 8 3
  • D 2 3

Q6:

Calculate 2 5 + 1 4 4 4 9 .

  • A 1 2 7
  • B 5 7
  • C 1 0 7
  • D 1 3 7
  • E 1 7 7

Q7:

Express ( 3 ) + 4 0 5 5 5 5 in its simplest form.

  • A 2 + 3 5
  • B 3 + 2 0 5
  • C 3 + 3 3 5
  • D 3 2 5
  • E 3 2 5

Q8:

Simplify 3 9 5 3 + 9 3 5 3 .

  • A 1 3 2 3 5
  • B 1 3 2 1 0 3
  • C 1 3 2 1 5
  • D 4 4 1 5
  • E 4 4 5

Q9:

Calculate 1 1 + 1 2 4 9 1 9 6 .

Q10:

Calculate 1 4 + 2 5 1 6 7 6 2 0 .

  • A 2 1 1 6
  • B 1 4
  • C 1 7 6 0
  • D 5 1 6
  • E 1 8

Q11:

Given that 𝑥 = 3 + 7 , find the value of 𝑥 + 4 𝑥 + 4 4 2 .

  • A 3 2 + 5 7
  • B 1 2 + 1 0 7
  • C102
  • D 3 2 + 1 0 7
  • E70

Q12:

Simplify 1 1 3 1 3 5 + 1 5 7 1 7 9 + 1 9 1 1 .

  • A 1 1 1 2
  • B 1 + 1 1 2
  • C 1 + 1 1
  • D 1 1 1 2
  • E 1 + 1 1

Q13:

Given that 𝑥 = 1 6 5 and 𝑦 = 6 5 , find ( 𝑥 + 𝑦 ) .

Q14:

What is the conjugate of 1 1 + 9 4 9 4 ? Express your answer in simplest form.

  • A 9 4 1 1
  • B 1 1 + 9 4
  • C 9 4
  • D 1 1 9 4
  • E 9 4 9 4

Q15:

What is the conjugate of 𝑥 = 2 + 5 ? Find the product of 𝑥 and its conjugate.

  • A 1 2 + 5 , 1 0
  • B 2 5 , 7
  • C 1 2 + 5 , 3
  • D 2 5 , 3
  • E 1 2 + 5 , 1

Q16:

What is the conjugate of 2 7 ? What is the product of 2 7 and its conjugate?

  • A 1 2 7 , 1 4
  • B 2 + 7 , 1 1
  • C 1 2 7 , 3
  • D 2 + 7 , 3
  • E 1 2 7 , 1

Q17:

Given that 𝑥 = 2 , find the value of 𝑥 + 2 .

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

Q18:

Simplify 8 1 0 1 0 ÷ 6 3 7 .

  • A 1 0 7
  • B 1 3
  • C 7 1 0
  • D3

Q19:

Express 4 0 3 0 0 3 0 in its simplest form.

  • A 2
  • B 3 1 0
  • C 3 0
  • D 1 0
  • E 3

Q20:

Given that 𝑥 = 1 , 5 2 1 2 2 5 , evaluate 𝑥 3 .

Q21:

Given that 𝑎 = 5 4 and 𝑏 = 2 5 8 1 , find 𝑎 𝑏 .

  • A 2 5 1 3
  • B 1 0 1 3
  • C 5 1 8
  • D 5 6

Q22:

Given that 𝑎 = 2 5 4 1 and 𝑏 = 4 1 2 5 , find 𝑎 𝑏 .

  • A1
  • B 4 1 2 0
  • C 2 2 0 5
  • D 2 0 4 1

Q23:

Calculate 1 3 1 2 3 .

  • A 3 5
  • B 4 5
  • C 2 3
  • D 1 3
  • E 1 2

Q24:

Calculate 1 6 9 × 1 2 0 .

  • A 1 1 2
  • B 4 3
  • C 5 2 3
  • D 1 1 5

Q25:

Calculate 4 × 8 1 × 4 × 8 1 .

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.