Question

find the smallest number by which 1420 must be multiplied so that the product becomes a perfect squre also find the square root of the perfect squre

Answer 1

answer is 2 thank you

Answer 2

Prime Factorisation of 1420:

1420 = 2² x 5 x 71

.

To make the number into a perfect square, the exponents must in multiples of 2.

.

Let k be the number that is needed to be multiplied.

.

Find k:

1420 = 2² x 5 x 71

1420k = 2² x 5² x71²

k = 5 x 71 = 355

.

Answer: The smallest number is 355

------------------------------------------------------------------------------------------

.

Find the number:

The perfect square is 1420k

1420k = 1420(355) = 504100

.

Find square root:

√ 504100 = 710

.

Answer: The square root of the prefect square is 710