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Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?
- a)3
- b)5
- c)9
- d)11
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Find the smallest number by which 396 must be multiplied so that the p...
396 = 2 × 2× 3 × 3 × 11
To make a perfect square, 11 is multiplied to 396.
To make a perfect square, 11 is multiplied to 396.
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Find the smallest number by which 396 must be multiplied so that the p...
To find the smallest number by which 396 must be multiplied so that the product becomes a perfect square, we need to analyze the prime factorization of 396.
Prime factorization of 396:
396 = 2^2 * 3^2 * 11
A perfect square is a number whose prime factors appear in pairs. In other words, each prime factor must have an even exponent.
To make 396 a perfect square, we need to multiply it by the smallest number that will give every prime factor an even exponent.
Let's consider each prime factor and its current exponent:
1. Prime factor 2: The exponent is 2, which is already even.
2. Prime factor 3: The exponent is 2, which is already even.
3. Prime factor 11: The exponent is 1, which is odd.
Since the exponent of the prime factor 11 is odd, we need to multiply 396 by 11 to make it a perfect square.
Therefore, the smallest number by which 396 must be multiplied so that the product becomes a perfect square is 11.
Hence, the correct answer is option D) 11.
Prime factorization of 396:
396 = 2^2 * 3^2 * 11
A perfect square is a number whose prime factors appear in pairs. In other words, each prime factor must have an even exponent.
To make 396 a perfect square, we need to multiply it by the smallest number that will give every prime factor an even exponent.
Let's consider each prime factor and its current exponent:
1. Prime factor 2: The exponent is 2, which is already even.
2. Prime factor 3: The exponent is 2, which is already even.
3. Prime factor 11: The exponent is 1, which is odd.
Since the exponent of the prime factor 11 is odd, we need to multiply 396 by 11 to make it a perfect square.
Therefore, the smallest number by which 396 must be multiplied so that the product becomes a perfect square is 11.
Hence, the correct answer is option D) 11.
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Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer?.
Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number by which 396 must be multiplied so that the product becomes a perfect square?a)3b)5c)9d)11Correct answer is option 'D'. Can you explain this answer?.
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