If (2^3\times3^x\times5^2) is a perfect square, which value of (x) is not possible?
Answer and explanation
Correct answer: None of the values is possible
Step 1: A perfect square requires all prime exponents to be even. Step 2: The exponent of (2) is already (3), which is odd, so changing only (x) cannot make the number a perfect square. Step 3: Check the whole prime factorisation, not only the unknown exponent.
Frequently asked questions
What is the correct answer to this question?
None of the values is possible
Why is this the correct answer?
Step 1: A perfect square requires all prime exponents to be even. Step 2: The exponent of (2) is already (3), which is odd, so changing only (x) cannot make the number a perfect square. Step 3: Check the whole prime factorisation, not only the unknown exponent.
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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