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Worksheet: Simplifying Radical Expressions

Q1:

Express 5 9 4 4 × 4 4 5 9 in its simplest form.

Q2:

Expand and simplify the expression 5 7 2 7 + 3 5 .

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

Q3:

Given that 𝑎 𝑏 = 𝑎 𝑏 , simplify 2 5 𝑥 4 .

  • A 𝑥 5 4
  • B 5 𝑥 4
  • C 2 5 𝑥 2
  • D 5 𝑥 2
  • E 𝑥 2 5 2

Q4:

Simplify 4 8 6 × 4 2 7 5 5 .

  • A 6 × 7 5 1 0
  • B 1 3 6
  • C54
  • D 1 4

Q5:

Write 8 + 2 in the form 𝑎 2 , where 𝑎 is an integer.

  • A 2 2
  • B 5 2
  • C 4 2
  • D 3 2
  • E 7 2

Q6:

Express 5 2 2 5 2 in the form 𝑎 𝑏 where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.

  • A 5 2 7
  • B 9 0 7
  • C 4 5 7
  • D 1 5 7
  • E 6 7

Q7:

Find the conjugate of 6 7 + 3 , then find the product of 6 7 + 3 and its conjugate.

  • A 1 6 7 + 3 , 126
  • B 6 7 3 , 255
  • C 1 6 7 + 3 , 249
  • D 6 7 3 , 249
  • E 1 6 7 + 3 , 1

Q8:

Calculate 9 × 4 4 + 3 5 2 6 + 5 0 + 1 1 × 1 4 + 1 7 6 ÷ 2 + 5 5 ÷ 1 1 4 .