## 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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## Answers ( )

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 which600should bemultipliedso that it becomes aperfect square.So, at first we’ll

resolve the given number into prime factorsby usingprime factorizationmethod. After that, we’llmake the pairsof common factors. Thenumberwhichcan’t begrouped into pairsis thesmallest number,with which600should bemultipliedso that it becomes aperfect square.Resolving 600 into prime factors,

We get that,

600 = 2 × 2 × 3 × 2 × 5 × 5

600 =

2 × 2× 3 × 2 ×5 × 5We get that

(3 × 2)left unpaired, so6is the smallest number, with which600should be multiplied so that it becomes a perfect square.## ❝

Extra❞Howtofindthesquarerootofanynumberusingprimefactorization?methodIn prime factorization method, firstly we find the prime factors of the given number by prime factorization. Then, we form pairs of like factors and from each pair we pick out one prime factor and then we multiply the the factors so picked , the product we get is the square root of the given number.