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If (n=2^{11}\times3^{10}\times5^7), by which smallest number should (n) be divided to make it a perfect cube?
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Answer and explanation
Correct answer: (2^2\times3\times5)
Step 1: In a perfect cube, every exponent must be a multiple of 3. Step 2: Reduce (2^{11}) to (2^9), (3^{10}) to (3^9), and (5^7) to (5^6). Step 3: So the smallest divisor is (2^2\times3\times5).
Frequently asked questions
What is the correct answer to this question?
(2^2\times3\times5)
Why is this the correct answer?
Step 1: In a perfect cube, every exponent must be a multiple of 3. Step 2: Reduce (2^{11}) to (2^9), (3^{10}) to (3^9), and (5^7) to (5^6). Step 3: So the smallest divisor is (2^2\times3\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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