Question

what is the smallest natural number by which 1792 should be multiplied so that it becomes a perfect square? method please answer​

Answer 1

Answer:

By using  prime factorization  method we get

1792=2×2×2×2×2×2×2×2×7

1792=(2^8)×7

square root on both sides

√1792=(2^4)×√7

to make it a perfect square we need even no. of sevens multiplied

(i.e even power on 7)

we have only  7^1

the nearest even power would be 7^2

1 more seven must be multiplied to make 7^1 to 7^2

∴7 must be multiplied to 1792 to make it a perfect square.

so, one