For the Following Number, Find the Smallest Whole Number by Which It Should Be Multiplied So as to Get a Perfect Square Number. Also Find the Square Root of the Square Number So Obtained. 180 - Mathematics

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

180

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Solution

180 can be factorised as follows.

180 = 2 × 2 × 3 × 3 × 5

Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.

180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5

Therefore, 180 × 5 = 900 is a perfect square.

∴ `sqrt(900)` 2 x 3 x 5 = 30

Concept: Finding Square Root Through Prime Factorisation

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Chapter 6: Squares and Square Roots - Exercise 6.3 [Page 102]

Q 5.2 Q 5.1 Q 5.3

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