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