Question

find the square root of each of the following by prime factorisation i - 225. ii - 441. iii - 529 iv - 40000. v - 7744 vi - 8281 vii - 4096. viii - 28900

40 points​

Answer 1

Answer:

I hope it's help you okkkk

Answer 2

Before solving the question, let us understand what is the procedure of finding square root by prime factorisation.

Merely, there are some steps which we have to follow in order to find square root.

Steps are:

1. Resolve the number into prime factors by successive divisions.
2. check out pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
3. Take out one factor from each created pair.
4. Find the product of factors obtained in above step.
5. product we get in 4th step is prime factor of that particular number.

We know the procedure, now, let's solve the question

i) 225 = 3 × 3 × 5 × 5 = 3 × 5 = 15

=> √225 = 15

ii) 441 = 3 × 3 × 7 × 7 = 3 × 7 = 21

=> √441 = 21

iii) 529 = 23 × 23 = 23

=> √529 = 23

iv) 40000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

=> 2 × 2 × 2 × 5 × 5 = 200

=> √40000 = 200

v) 7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11

=> 2 × 2 × 2 × 11 = 88

=> √7744 = 88

vi)8281 = 7 × 7 × 13 × 13 = 7 × 13 = 91

=> √8281 = 91

vii)4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

=> 2 × 2 × 2 × 2 × 2 × 2 = 64

=> √4096 = 64

viii)28900 = 2 × 2 × 5 × 5 × 17 × 17

=> 2 × 5 × 17 = 170

=> √28900 = 170

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