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Worksheet: Cube Root of a Rational Number

In this worksheet, we will practice finding the cube root of a rational number using factorization or calculators and solving equations that include a cube root.

Q1:

Evaluate 3 6 4 3 4 3 .

  • A 8 7
  • B 4 7 or − 4 7
  • C 8 7 or − 8 7
  • D 4 7
  • E 8 9

Q2:

Find the value of 3 3 6 4 2 7 − − 1 8 .

  • A 5
  • B 1 1 1 8
  • C − 2 3
  • D 1 1 6
  • E − 8 3

Q3:

Find the value of 3 √ 4 × 0 . 1 9 6 .

Q4:

Determine whether the cube root of a rational number, which is not a perfect cube, is a rational or an irrational number.

  • A an irrational number
  • B a rational number

Q5:

Solve 𝑥 = 2 7 8 3 .

  • A 𝑥 = 3 8
  • B 𝑥 = 3 2 or 𝑥 = − 3 2
  • C 𝑥 = 3 8 or 𝑥 = − 3 8
  • D 𝑥 = 3 2
  • E 𝑥 = 9 2

Q6:

Calculate √ 0 . 0 0 0 3 6 1 + 5 . 9 8 1 .

Q7:

Find the value of 3 √ 0 . 0 2 7 .

Q8:

Find the value of 3 √ − 0 . 0 0 0 5 1 2 .

Q9:

Find the value of 3 4 1 2 ÷ 1 0 2 3 .

  • A 3 4 , − 3 4
  • B 4 3
  • C 4 3 , − 4 3
  • D 3 4
  • E 9 1 6

Q10:

Given that 𝑥 8 + 7 = 1 3 , find the value of 𝑥 , and state whether it is a rational or irrational number.

  • A4, irrational
  • B 2 √ − 6 3 , rational
  • C4, rational
  • D 2 √ − 6 3 , irrational
  • E − 4 8 , irrational

Q11:

Find the value of 3 3 − 1 0 0 0 7 2 9 + 2 7 1 0 0 0 .

  • A − 7 1 9
  • B − 7 3 2 7 0
  • C − 1 3
  • D − 7 3 9 0
  • E − 1 0 0 2 7

Q12:

Express 3 3 √ 2 5 6 2 − 4 2 7 in its simplest form.

  • A 2 √ 4 3
  • B 3 √ 4 6
  • C 3 √ 4 3
  • D 5 √ 4 3 3

Q13:

If possible, find the value of 𝑥 which satisfies − 0 . 2 1 6 𝑥 = 2 7 3 , given that 𝑥 is in ℚ .

  • A − 2 0
  • BNo value exists.
  • C − 9 5
  • D − 5
  • E − 1 5

Q14:

Evaluate 3 3 √ − 2 7 + √ − 0 . 1 2 5 + 5 1 1 6 .

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

Q15:

Find the value of 3 3 − 2 7 8 × 2 7 6 4 .

  • A − 2
  • B − 9 2
  • C 0
  • D − 9 8
  • E − 3 2

Q16:

Which of the following is true?

  • A
  • B
  • C
  • D

Q17:

Determine whether the cubic root of a perfect cube is a rational or an irrational number.

  • A a rational number
  • B an irrational number

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