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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticExpertLevel 6
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What is the smallest number by which 60480 must be multiplied to get a perfect cube?

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Answer and explanation

Correct answer: 1225

Step 1: (60480=2^6\times3^3\times5\times7). Step 2: For a perfect cube, every exponent must be a multiple of 3. Step 3: Powers of 5 and 7 are 1, so multiply by (5^2\times7^2=1225).

Related tags

Perfect-CubePrime-FactorisationExpert

Frequently asked questions

What is the correct answer to this question?

1225

Why is this the correct answer?

Step 1: (60480=2^6\times3^3\times5\times7). Step 2: For a perfect cube, every exponent must be a multiple of 3. Step 3: Powers of 5 and 7 are 1, so multiply by (5^2\times7^2=1225).

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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