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
View Answer

Answer: a
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.
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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
View Answer

Answer: b
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
View Answer

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

Answer: d
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
View Answer

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

Answer: a
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
View Answer

Answer: d
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.
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8. Evaluate \(\sqrt[3]{15625}\).
a) 35
b) 25
c) 45
d) 15
View Answer

Answer: b
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 \(\sqrt[3]{9261}\).
a) 51
b) 21
c) 29
d) 39
View Answer

Answer: b
Explanation: ∛x represents cube root of number x. Factorizing 9261 we get:
9261 = 21×21×21
The cube root of 9261 is 21.
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10. 673 = _____
a) 300733
b) 300753
c) 300763
d) 300793
View Answer

Answer: c
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter