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

Start Practicing

Worksheet: Operations with Radicals

Q1:

Express 3 3 2 5 6 4 in its simplest form.

  • A 4 3
  • B3
  • C 3 4 3
  • D 3 4 3

Q2:

Given that 𝑥 = 6 3 5 6 + 3 5 and 𝑦 = 3 9 6 2 3 5 , determine the value of 𝑥 + 𝑦 expressing your answer in simplest form.

  • A 1 2 2 + 1
  • B 1 2 2 + 7 1 2 4 3 5
  • C 1 2 2 + 7 1 + 2 4 3 5
  • D 1 2 2 + 7 1

Q3:

Given that 𝑥 = 4 1 5 4 + 1 5 and 𝑦 = 9 6 3 1 5 , determine the value of 𝑥 + 𝑦 expressing your answer in simplest form.

  • A 8 3 + 1
  • B 8 3 + 3 1 1 6 1 5
  • C 8 3 + 3 1 + 1 6 1 5
  • D 8 3 + 3 1

Q4:

Given that 𝑎 = 6 4 and 𝑏 = 6 4 , find the value of 𝑎 + 𝑏 .

  • A 2 6 4
  • B 2 6
  • C 0
  • D 2 6 8
  • E 8

Q5:

Given that 𝑎 = 6 6 + 1 and 𝑏 = 6 6 1 , find the value of 𝑎 + 𝑏 2 2 .

Q6:

Calculate 2 2 × 4 7 1 1 ÷ 8 2 7 7 .

  • A 7 2 2
  • B 1 2 8 7 7
  • C 4 9 2 2
  • D 4 9 1 1
  • E 7 1 1

Q7:

Given that 𝑥 = 1 2 + 1 0 1 0 and 𝑦 = 1 0 1 2 1 0 , find 𝑥 𝑦 expressing your answer in simplest form.

  • A 1 3 2 0 4 4 1 0
  • B 1 2 0 + 1 2 0 1 0
  • C 1 0 8 0 + 2 4 4 1 0
  • D 1 0 8 0 4 4 1 0
  • E 1 3 2 0 + 2 4 4 1 0

Q8:

Given that 𝑥 = 2 3 and 𝑦 = 2 + 3 , find 𝑥 + 𝑦 𝑥 𝑦 1 expressing your answer in simplest form.

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

Q9:

Given that 𝑥 = 1 4 2 + 1 7 and 𝑦 = 1 4 2 1 7 , find ( 𝑥 + 𝑦 ) 2 .

Q10:

Given that 𝑥 = 3 and 𝑦 = 6 , find the value of 𝑥 + 𝑦 𝑥 𝑦 2 .

  • A 5 + 6
  • B 1 5 + 3 6
  • C 4 9 + 2 0 6
  • D 4 9 2 0 6
  • E 4 9 + 1 0 6

Q11:

Express 5 5 4 3 2 0 3 3 in its simplest form.

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

Q12:

What is the value of 2 ÷ 2 2 + 3 6 × 6 5 ?

Q13:

Express 4 3 2 + 1 5 1 5 4 5 6 1 2 in its simplest form.

  • A 6 1 2
  • B 1 9 2
  • C 1 3 5
  • D 1 3 2

Q14:

Given that 𝑥 = 7 + 5 and 𝑦 = 2 𝑥 , find 𝑥 + 𝑦 𝑥 𝑦 expressing your answer in simplest form.

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

Q15:

Given that 𝑎 = 5 + 7 and 𝑏 = 5 7 , find 𝑎 𝑏 .

Q16:

Express 1 1 2 + 2 0 2 + 5 × 1 0 in its simplest form.

  • A 2 6 5
  • B 2 1 2
  • C 2 6 1 0
  • D 2 6 2
  • E 6 2

Q17:

Express 3 3 3 7 2 + 7 2 9 1 8 1 6 5 7 6 in its simplest form.

  • A 5 5 9 3
  • B 1 0 7 9 3
  • C 5 5 9 3
  • D 1 0 7 9 3

Q18:

Express 3 3 3 1 2 8 + 4 3 2 2 1 4 in its simplest form.

  • A 1 1 2 3
  • B 9 2 3
  • C 1 1 2 3
  • D 9 2 3

Q19:

Express 3 3 3 5 ÷ 2 5 9 in its simplest form.

  • A 5 3
  • B 9 2 5
  • C 15
  • D 3 5

Q20:

Given that 𝑥 = 1 3 2 and 𝑦 = 3 2 , find ( 𝑥 𝑦 ) 2 .

Q21:

Given that 𝑎 = 5 + 8 and 𝑏 = 5 8 , find the value of 𝑎 + 𝑏 .

  • A 16
  • B 69
  • C 5 9
  • D 2 5

Q22:

Evaluate 1 0 0 2 1 6 3 .

Q23:

Simplify 2 4 8 + 1 0 6 1 3 .

  • A 4 6 + 4
  • B 4 6
  • C 4 6 4
  • D 4 6
  • E4

Q24:

Determine the value of 5 1 6 2 5 1 1 3 9 1 2 5 1 4 3 3 3 3 .

  • A 4 1 + 3 3 3
  • B 4 9 2 5 3 3
  • C 5 2 5 3 3
  • D 4 1 2 5 3 3
  • E 4 1 1 1 3 3

Q25:

Express 5 6 9 6 + 4 6 + 6 3 3 in its simplest form.

  • A 5 6
  • B 8 6 + 9 6 3
  • C 4 6 + 5 6 3
  • D 9 6 8 6 3
  • E 9 6 1 0 6 3