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If (n=2^{10}\times3^8\times5^6), by which smallest number should (n) be divided to make it a perfect cube?
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Answer and explanation
Correct answer: (2\times3^2)
Step 1: In a perfect cube, every exponent must be a multiple of 3. Step 2: Reduce (2^{10}) to (2^9) by dividing by 2, and (3^8) to (3^6) by dividing by (3^2). Step 3: The smallest divisor is (2\times3^2).
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What is the correct answer to this question?
(2\times3^2)
Why is this the correct answer?
Step 1: In a perfect cube, every exponent must be a multiple of 3. Step 2: Reduce (2^{10}) to (2^9) by dividing by 2, and (3^8) to (3^6) by dividing by (3^2). Step 3: The smallest divisor is (2\times3^2).
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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