Worksheet: Operations with Radicals

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

Q1:

Express 2 5 6 4 in its simplest form.

  • A 4
  • B3
  • C 3 4
  • D 3 4

Q2:

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

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

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:

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

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

Q5:

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

Q6:

Simplify 2 4 8 + 1 0 6 1 .

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

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

Q11:

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

Q12:

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

Q13:

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

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

Q16:

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

  • 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

Q17:

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

Q18:

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

Q19:

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

Q20:

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

Q21:

Evaluate 1 0 0 2 1 6 .

Q22:

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

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

Q23:

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

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

Q24:

Find the value of 4 7 5 + 4 7 5 .

  • A 9 2 , 7 7 8 1 2 5
  • B 9 4 5
  • C 2 , 2 0 9 2 5
  • D0

Q25:

Given that 𝑥 = 7 6 and 𝑦 = 7 + 6 , find the value of 𝑥 𝑦 𝑦 ( 𝑥 + 𝑦 ) .

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