Question

The smallest whole number by which 252 should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

Answer 1

Answer:

Smallest number to multiply is 7 and square root of square number is 42..

Step-by-step explanation:

1) We first find the prime factors of 252 By prime factorization.

Hence,

252 = 2 x 2 x 3 x 3 x 7

= (2×2)×(3×3)×7

Here, we see that 2 and 3 occur  in pairs but 7 needs a pair. Hence, the given number is not a perfect square.

If We now multiply 252 by 7 then we get

252×7= 1764 = (2×2)×(3×3)×(7×7)

 Therefore,the number 252 has 3 pairs of equal prime factors .

Hence, 1764 is a perfect square &

√1764= 2×3×7=42

Hence, the smallest number by which 1764 must be multiplied so that the product is a perfect square is 7.

And the square root of the new number is √1764=42.

Hope it helps................