Which is the smallest number, with which 600 should be multiplied so that it becomes a perfect square?
Question
Which is the smallest number, with which 600 should be multiplied so that it becomes a perfect square?
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Mathematics
2 years
2021-07-08T04:23:57+00:00
2021-07-08T04:23:57+00:00 2 Answers
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Answer:
Step-by-step explanation:
Given,
The smallest number, with which 600 should be multiplied so that it becomes a perfect square.
Answer is 6.
Because, 6 × 600 = 3600
Square root of √3600 = √60 × √60 = (√60)^2 = 60
∴ 3600 is a perfect square
∴The smallest number = 6
Here, we are asked to find the smallest number, with which 600 should be multiplied so that it becomes a perfect square.
So, at first we’ll resolve the given number into prime factors by using prime factorization method. After that, we’ll make the pairs of common factors. The number which can’t be grouped into pairs is the smallest number, with which 600 should be multiplied so that it becomes a perfect square.
Resolving 600 into prime factors,
We get that,
We get that (3 × 2) left unpaired, so 6 is the smallest number, with which 600 should be multiplied so that it becomes a perfect square.
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