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How many factors of (2^4 \times 3^2 \times 5) are perfect squares?
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Answer and explanation
Correct answer: 6
Step 1: In a square factor, every prime exponent must be even. Step 2: For (2), choices are (0,2,4), so (3); for (3), choices are (0,2), so (2); for (5), only (0), so (1). Total (3 \times 2 \times 1=6). Step 3: Count even exponent choices separately.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Step 1: In a square factor, every prime exponent must be even. Step 2: For (2), choices are (0,2,4), so (3); for (3), choices are (0,2), so (2); for (5), only (0), so (1). Total (3 \times 2 \times 1=6). Step 3: Count even exponent choices separately.
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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