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If (N=2^{10}\times3^8\times5^5\times7), by which smallest number must (N) be multiplied to make it a perfect cube?
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Answer and explanation
Correct answer: (2^2\times3\times5\times7^2)
Step 1: For a perfect cube, every exponent must be a multiple of 3. Step 2: We must make 10 to 12, 8 to 9, 5 to 6, and 1 to 3. Step 3: So the smallest multiplier is (2^2\times3\times5\times7^2).
Frequently asked questions
What is the correct answer to this question?
(2^2\times3\times5\times7^2)
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 10 to 12, 8 to 9, 5 to 6, and 1 to 3. Step 3: So the smallest multiplier is (2^2\times3\times5\times7^2).
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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