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What is the smallest number by which 30240 must be multiplied to get a perfect cube?
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Answer and explanation
Correct answer: 2450
Step 1: (30240=2^5\times3^3\times5\times7). Step 2: For a perfect cube, exponents must be multiples of 3. Step 3: We need (2), (5^2), and (7^2), so the smallest multiplier is (2\times25\times49=2450).
Frequently asked questions
What is the correct answer to this question?
2450
Why is this the correct answer?
Step 1: (30240=2^5\times3^3\times5\times7). Step 2: For a perfect cube, exponents must be multiples of 3. Step 3: We need (2), (5^2), and (7^2), so the smallest multiplier is (2\times25\times49=2450).
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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