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If a number has prime factorisation (2^{12}\times3^8\times5^5), 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: (3\times5)
Step 1: For a perfect cube, exponents must be multiples of 3. Step 2: (2^{12}) is already suitable, while (3^8) and (5^5) must become (3^9) and (5^6). Step 3: The smallest multiplier is (3\times5).
Frequently asked questions
What is the correct answer to this question?
(3\times5)
Why is this the correct answer?
Step 1: For a perfect cube, exponents must be multiples of 3. Step 2: (2^{12}) is already suitable, while (3^8) and (5^5) must become (3^9) and (5^6). Step 3: The smallest multiplier is (3\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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