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By what least number 384 be multiplied so that the product may be a perfect square?
- a)2
- b)5
- c)4
- d)6
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
By what least number 384 be multiplied so that the product may be a pe...
∴ 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
so it lacks a 2 and 3
∴ Required number = 6
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By what least number 384 be multiplied so that the product may be a pe...
Understanding the Problem:
To find the least number by which 384 can be multiplied so that the product becomes a perfect square.
Solution:
To make the product a perfect square, we need to find the factors of 384 that will result in a perfect square.
- The prime factorization of 384 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 2.
- To make it a perfect square, we need to balance the powers of each prime factor.
- In this case, we need to balance the power of 3.
- So, we need to multiply 384 by 3 to make it a perfect square.
Therefore, the least number by which 384 can be multiplied to get a perfect square is 6 (3 x 384 = 1152, which is a perfect square).
Therefore, the correct answer is option 'D' (6).
To find the least number by which 384 can be multiplied so that the product becomes a perfect square.
Solution:
To make the product a perfect square, we need to find the factors of 384 that will result in a perfect square.
- The prime factorization of 384 is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 2.
- To make it a perfect square, we need to balance the powers of each prime factor.
- In this case, we need to balance the power of 3.
- So, we need to multiply 384 by 3 to make it a perfect square.
Therefore, the least number by which 384 can be multiplied to get a perfect square is 6 (3 x 384 = 1152, which is a perfect square).
Therefore, the correct answer is option 'D' (6).
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By what least number 384 be multiplied so that the product may be a perfect square?a)2b)5c)4d)6Correct 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 By what least number 384 be multiplied so that the product may be a perfect square?a)2b)5c)4d)6Correct 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 By what least number 384 be multiplied so that the product may be a perfect square?a)2b)5c)4d)6Correct answer is option 'D'. Can you explain this answer?.
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