# Mathematics Questions and Answers – Cube Root through Prime Factorisation

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Cube Root through Prime Factorisation”.

1. Find the prime factors of 6.
a) 2, 3
b) 2, 5
c) 3, 5
d) 5, 7

Explanation: A prime number can only be divided by 1 or itself, so it cannot be factored any further. On multiplying 2 and 3, we get 6. 2 and 3 cannot be factored further. Hence, 2 and 3 are prime factors of 6.

2. Find prime factors of 72.
a) 2×2×7×7
b) 2×2×2×3×3
c) 2×3×5×7×7
d) 2×2×2×3×7

Explanation: When factorizing 72 we get,
72 = 2×36
72 = 2×2×18
72 = 2×2×2×9
72 = 2×2×2×3×3.

3. Which number should be multiplied to 392 to obtain perfect cube?
a) 7
b) 9
c) 8
d) 2

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 392 we get:
392 = 2×2×2×7×7
When 392 is multiplied with 7, we get a perfect cube.

4. Find the cube root of 729.
a) 3
b) 7
c) 5
d) 9

Explanation: Factorizing 729 we get:
729 = 3×243
729 = 3×3×81
729 = 3×3×9×9
729 = 9×9×9
Thus, cube root of 729 is 9.

5. What multiplied to 68600 gives a perfect cube?
a) 7
b) 2
c) 5
d) 9

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 68600 we get:
68600 = 2×2×2×5×5×7×7×7
When 68600 is multiplied with 5, we get a perfect cube.

6. What is the cube root of 216000?
a) 60
b) 70
c) 80
d) 90

Explanation: Factorizing 216000 we get:
21600 = 2×2×2×3×3×3×10×10×10
The cube root of 216000 is 60.

7. Which of below is not a perfect cube?
a) 1331
b) 2197
c) 4913
d) 5508

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. For example, 11 is a natural number which multiplied with itself thrice gives us 1331. Hence, 1331 is a perfect cube. But we do not have a natural number which multiplied with itself thrice gives us 5508. Hence, 5508 is not a perfect cube.

8. Evaluate $$\sqrt{15625}$$.
a) 35
b) 25
c) 45
d) 15

Explanation: ∛x represents cube root of number x. Factorizing 15625 we get:
15625 = 25×25×25
The cube root of 15625 is 25.

9. Evaluate $$\sqrt{9261}$$.
a) 51
b) 21
c) 29
d) 39

Explanation: ∛x represents cube root of number x. Factorizing 9261 we get:
9261 = 21×21×21
The cube root of 9261 is 21.

10. 673 = _____
a) 300733
b) 300753
c) 300763
d) 300793

Explanation: In order to calculate the cube of 67 we use the formula,
(a-b)3, where we consider a=70 and b=3
Therefore (70-3)3 = 703 – 3 × 702 × 3 + 3 × 70 × 32 – 33
Therefore (70-3)3 = 343000 – 44100 + 1890 – 27
Therefore (70-3)3 = 300763.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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