Question

find the square root of each the following by prime factorisation
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Answer 1

Square Root of a Perfect Square by using the Prime Factorization Method

484 = 2 × 2 × 11 × 11. √484 = √(2 × 2 × 11 × 11) ...

324 = 2 × 2 × 3 × 3 × 3 × 3. √324 = √(2 × 2 × 3 × 3 × 3 × 3) ...

1764 = 2 x 2 x 3 x 3 x 7 x 7. ...

4356 = 2 x 2 x 3 x 3 x 11 x 11. ...

11025 = 5 x 5 x 3 x 3 x 7 x 7. ...

= 5 × 5 × 3 × 3 × 3 × 3.

Hint: To find the square root of a given number by prime factorization method, we will start dividing the number by the smallest prime number which is a factor of the given number until we get all the factors of the number. Prime factorization is done by writing all the factors of a number which are prime.