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Worksheet: Operations with Cube Roots

Q1:

Simplify 3 3 1 8 + 1 8 .

  • A 18
  • B 3 3 6
  • C 3 1 8
  • D 2 1 8 3

Q2:

Express 3 3 3 3 2 9 × 6 + 2 1 4 in its simplest form.

  • A 2 3
  • B 5 2 3
  • C5
  • D 5 2 3

Q3:

Express 3 3 4 × 1 6 in its simplest form.

Q4:

Express 4 5 4 9 3 in the form 𝑎 𝑏 3 where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.

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

Q5:

Given that 𝑥 = 6 1 0 3 and 𝑦 = 6 + 1 0 3 , find the value of 𝑥 + 𝑦 2 2 .

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

Q6:

Express 5 1 9 2 + 5 6 4 8 + 3 7 5 3 3 3 in its simplest form.

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

Q7:

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

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

Q8:

Express 3 1 2 5 0 in the form 𝑎 𝑏 3 where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.

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

Q9:

Find the value of 6 4 4 8 6 5 6 3 3 expressing your answer in the simplest form.

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

Q10:

Express 3 3 2 5 6 2 0 2 1 7 1 6 in its simplest form.

  • A 2 1 7 1 6 3
  • B 3 9 4 3
  • C 5 2 3 5 7 1 6 3
  • D 3 1 4 3

Q11:

Find the value of 3 3 1 1 2 5 ÷ 2 7 1 0 0 0 .

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

Q12:

Simplify 4 6 ÷ 3 6 6 6 + 6 + 3 3 2 .

  • A8
  • B 8 5
  • C 4 5
  • D 8 1 5

Q13:

Express 3 3 1 2 × 1 4 in its simplest form.

  • A 4
  • B 1 4
  • C 2
  • D 1 2

Q14:

Given that 𝑥 = 4 and 𝑦 = 3 8 5 3 , find the value of 𝑥 𝑦 3 .

  • A 6 4 3 8 5
  • B 6 4 3 8 5
  • C 6 4 3 8 5
  • D 6 4 3 8 5

Q15:

Express 4 6 4 8 3 in the form 𝑎 𝑏 3 where 𝑎 and 𝑏 are integers and 𝑏 takes the least possible value.

  • A 2 4 3 3
  • B 3 2 4 3
  • C 3 2 4 3
  • D 2 4 3 3
  • E 6 3 3

Q16:

Calculate 3 5 3 3 .

Q17:

Express 3 3 6 4 8 1 in its simplest form.

  • A 4 3 3 3
  • B 4 + 3 3 3
  • C 4 + 3 3 3
  • D 4 3 3 3

Q18:

Express 1 7 3 × 4 9 9 3 3 in its simplest form.

Q19:

Determine the value of 3 0 . 7 2 9 × 7 2 9 .

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

Q20:

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

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

Q21:

Express 3 3 3 4 3 2 6 8 6 1 2 8 in its simplest form.

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

Q22:

Given that 𝑎 = 5 5 3 and 𝑏 = 5 + 5 3 , find the value of ( 𝑎 𝑏 ) 5 .

Q23:

Given that 𝑎 = 5 4 3 and 𝑏 = 5 + 4 3 , find the value of ( 𝑎 + 𝑏 ) 3 .

Q24:

Express 5 5 0 0 × 5 0 0 ÷ ( 1 6 × 7 5 ) 3 3 3 in its simplest form.

  • A 3 5
  • B 15
  • C 60
  • D 5 3

Q25:

Express 3 3 3 1 2 8 + 6 1 4 + 3 5 4 in its simplest form.

  • A 7 2 3
  • B 1 6 2 3
  • C 4 2 3
  • D 1 0 2 3