Question

find the smallest number by which 1058 must be multiplied so that the product becomes a perfect square. Also, find the square root of the perfect square​

Answer 1

Given: The number 1058

To find: the smallest number by which 1058 must be multiplied so that the product becomes a perfect square.

Solution:

• Now we have given the number 1058.

• By prime factorisation, the factors are:

                2   | 1058

                 23 | 529

                 23 | 23

                       | 1

                1058 = 23 x 23 x 2

• So the smallest number that should be multiplied is 2 so as to make perfect square.

                1058 x 2 = 2116

• And the square root of 2116 is 23 x 2 = 46.

Answer:

                  So the smallest number by which 1058 must be multiplied so that the product becomes a perfect square is 2, and the square root is 46.