If (N=2^2 \times 3^5), what is the smallest perfect-cube multiple of (N)?
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Answer and explanation
Correct answer: (2^3 \times 3^6)
Step 1: In a perfect cube, exponents must be multiples of (3). Step 2: (2^2) must become (2^3), and (3^5) must become (3^6). Step 3: For the smallest cube multiple, move each exponent to the next multiple of (3).
Frequently asked questions
What is the correct answer to this question?
(2^3 \times 3^6)
Why is this the correct answer?
Step 1: In a perfect cube, exponents must be multiples of (3). Step 2: (2^2) must become (2^3), and (3^5) must become (3^6). Step 3: For the smallest cube multiple, move each exponent to the next multiple of (3).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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