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Finding Cube Roots Quiz - CBSE Class 8 Mathematics

Free practice quiz: Finding Cube Roots (CBSE Class 8 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 20 multiple-choice questions on Finding Cube Roots, and 20 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Meaning of a Cube Root

  • The cube root of n is the number which, multiplied by itself three times, gives n.
  • Finding a cube root is the reverse of cubing a number.
  • Cube roots are written with the symbol ∛ (a root sign with a small 3).
Definition
\[\sqrt[3]{n}=x \iff x^3=n\]
Cube and cube root undo each other
\[\sqrt[3]{x^3}=x\]
Cube of a number
\[x^3=x\times x\times x\]

Common mistake: Confusing cube root with dividing by 3. The cube root of n is not n ÷ 3.

Prime Factorisation Method

  • Write the number as a product of prime factors.
  • Make groups of three equal prime factors. Take one factor from each group and multiply them.
  • If any prime factor is left without a full group of three, the number is not a perfect cube.
Triplets of primes
\[\sqrt[3]{p^3\times q^3}=p\times q\]
Powers in multiples of three
\[\sqrt[3]{a^{3m}}=a^{m}\]

Common mistake: Grouping equal prime factors in pairs, as for square roots, instead of in groups of three.

Cube Root of a Product

  • The cube root of a product equals the product of the cube roots.
  • Find the cube root of each factor separately, then multiply the results.
Product rule
\[\sqrt[3]{a\times b}=\sqrt[3]{a}\times\sqrt[3]{b}\]
Quotient rule
\[\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}\]

Common mistake: Adding the cube roots of the factors instead of multiplying them.

Estimation Method for Perfect Cubes

  • Mark off the last three digits of the perfect cube. The units digit of the cube gives the root's units digit.
  • Units digits 2 and 8 swap, and 3 and 7 swap. Every other digit stays the same.
  • For the part left after the last three digits, find the largest k with k³ not more than it. Then k is the tens digit.
Tens digit rule
\[k^3\le \text{remaining part}<(k+1)^3\]

Common mistake: Choosing a tens digit k whose cube is greater than the remaining part, or forgetting that 2↔8 and 3↔7 swap.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the cube root of 64?

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    Answer: A. 4

    Since 4 x 4 x 4 = 64, the cube root of 64 is 4.

  2. Calculate the cube root of 1728.

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    Answer: A. 12

    Since 12 x 12 x 12 = 1728, the cube root of 1728 is 12.

  3. Determine the cube root of 5832.

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    Answer: A. 18

    Since 18 x 18 x 18 = 5832, the cube root of 5832 is 18.

  4. Calculate the cube root of 46656.

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    Answer: A. 36

    Since 36 x 36 x 36 = 46656, the cube root of 46656 is 36.

  5. Determine the cube root of 2406104.

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    Answer: B. 134

    Since 134 x 134 x 134 = 2406104, the cube root of 2406104 is 134.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Find the cube root of 125.
  2. What is the cube root of 216?
  3. Find the cube root of 729.
  4. What is ³√3375?
  5. Find the cube root of 4096.
  6. What is the cube root of 13824?
  7. Find x if x³ = 9261.
  8. What is the cube root of 15625?
  9. Find ³√2744.
  10. Find x if x³ = 68921.
  11. What is ³√110592?
  12. Find the cube root of 175616.
  13. Calculate ³√32768.
  14. Find the cube root of a number which when multiplied by itself twice gives 12167.
  15. What is the cube root of (27 x 64)?

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