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Worksheet: Rationalizing Radical Expressions

Q1:

Simplify 1 2 5 2 3 1 3 5 by rationalising the denominator.

  • A 3 7 6 5
  • B 1 2 2 3 5 1 3
  • C 1 1 5 6 5
  • D 6 0 2 3 5 6 5

Q2:

Simplify 9 3 + 1 0 1 1 3 by rationalising the denominator.

  • A 3 7 3 3
  • B 9 + 1 0 3 1 1
  • C 1 9 3 3 3
  • D 2 7 + 1 0 3 3 3

Q3:

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

  • A 56
  • B 8
  • C 2 2
  • D 2 7
  • E 28

Q4:

Given that 𝑥 = 2 5 3 and 𝑦 = 5 3 , find 𝑥 + 𝑦 expressing your answer in simplest form.

  • A 60
  • B 12
  • C 2 3
  • D 2 5
  • E 20

Q5:

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

  • A 3 1 3
  • B 3 7
  • C 3 7
  • D 3 1 3

Q6:

Given that 𝑥 = 3 0 6 , 𝑦 = 2 1 6 + 3 , and 𝑧 = 3 0 0 + 6 , find the value of ( 𝑥 𝑦 + 𝑧 ) 2 expressing your answer in simplest form.

Q7:

What is the conjugate of 1 2 1 1 + 4 3 ? Express your answer in simplest form.

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

Q8:

Simplify 2 0 7 3 by rationalizing the denominator.

  • A 2 0 7
  • B 2 0 7 4 9 3
  • C 2 0 7
  • D 2 0 7 4 9 3

Q9:

Given that 𝑎 = 9 5 7 𝑥 and 𝑎 = 2 9 𝑦 , find the value of 𝑎 𝑥 + 𝑦 .

  • A 9 5 7 + 2 9
  • B 9 5 7 2 9
  • C 9 5 7 2 9
  • D 3 3 2 9

Q10:

Given that 𝑥 = 2 5 + 2 2 7 and 𝑦 = 5 3 2 4 2 , find the value of 𝑥 + 𝑦 2 2 .

  • A 4 3 + 2 7 1 0
  • B 5 2 1
  • C 4 3 2 7 1 0
  • D 4 3
  • E 1 1 3 8 4

Q11:

Given that 𝑥 = 1 2 + 7 and 𝑦 = 1 9 2 + 1 1 2 , express 𝑥 in terms of 𝑦 .

  • A 𝑦 1 6
  • B 4 𝑦
  • C 1 6 𝑦
  • D 𝑦 4
  • E 𝑦 4

Q12:

Simplify 2 0 1 9 2 0 + 1 9 2 0 + 1 9 2 0 1 9 .

  • A78
  • B 8 9 5
  • C 7 8
  • D 8 9 5

Q13:

Given that 𝑥 = 7 1 3 and 𝑦 = 1 3 7 , find 1 8 2 ( 𝑥 + 𝑦 ) expressing your answer in simplest form.

  • A 1 8 2 9 1
  • B 1 8 2 7 + 1 8 2 1 3
  • C 2 0 9 1
  • D 4 0 9 1
  • E 2 9 1

Q14:

Express 2 1 6 6 1 1 in its simplest form.

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