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If a number has prime factorisation (2^5\times3^2\times5^4), what is the smallest number by which it must be multiplied to make a perfect cube?
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Answer and explanation
Correct answer: (2^2\times3\times5)
Step 1: For a perfect cube, exponents must be multiples of 3. Step 2: We need (2), (3), and (5^2) to make the powers (6,3,6). Step 3: The smallest multiplier is (2\times3\times5^2).
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, exponents must be multiples of 3. Step 2: We need (2), (3), and (5^2) to make the powers (6,3,6). Step 3: The smallest multiplier is (2\times3\times5^2).
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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