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If (N=2^4\times3^5\times5^2), by which smallest number must (N) be multiplied to make it a perfect cube?
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Answer and explanation
Correct answer: (2^2\times3\times5)
Step 1: For a perfect cube, every exponent must be a multiple of 3. Step 2: To make powers (4,5,2) into (6,6,3), we need (2^2), (3), and (5). Step 3: So the smallest multiplier is (2^2\times3\times5).
Frequently asked questions
What is the correct answer to this question?
(2^2\times3\times5)
Why is this the correct answer?
Step 1: For a perfect cube, every exponent must be a multiple of 3. Step 2: To make powers (4,5,2) into (6,6,3), we need (2^2), (3), and (5). Step 3: So the smallest multiplier is (2^2\times3\times5).
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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