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If (N=2^3 \times 3^2 \times 5), what is the smallest perfect-square multiple of (N)?
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Answer and explanation
Correct answer: (2^4 \times 3^2 \times 5^2)
Step 1: In a perfect square, all exponents must be even. Step 2: Make (2^3) into (2^4) and (5) into (5^2); (3^2) is already fine. Step 3: For the smallest square multiple, increase only the necessary exponents.
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What is the correct answer to this question?
(2^4 \times 3^2 \times 5^2)
Why is this the correct answer?
Step 1: In a perfect square, all exponents must be even. Step 2: Make (2^3) into (2^4) and (5) into (5^2); (3^2) is already fine. Step 3: For the smallest square multiple, increase only the necessary exponents.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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