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If (N=2^8\times3^7\times5^4\times7^2), by which smallest number must (N) be multiplied to make it a perfect cube?
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Answer and explanation
Correct answer: (2\times3^2\times5^2\times7)
Step 1: For a perfect cube, every exponent must be a multiple of 3. Step 2: We must make 8 to 9, 7 to 9, 4 to 6, and 2 to 3. Step 3: So the smallest multiplier is (2\times3^2\times5^2\times7).
Frequently asked questions
What is the correct answer to this question?
(2\times3^2\times5^2\times7)
Why is this the correct answer?
Step 1: For a perfect cube, every exponent must be a multiple of 3. Step 2: We must make 8 to 9, 7 to 9, 4 to 6, and 2 to 3. Step 3: So the smallest multiplier is (2\times3^2\times5^2\times7).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Fundamental Theorem of Arithmetic.
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