1458 smallest whole number by which it should be multiplied so as to get a perfect square number. also find the square root of the square number obtained

9514 1404 393

Step-by-step explanation:

The prime factorization of 1458 is ...

  1458 = 2·3^6

The exponent of 3 is even, but we need another factor of 2 to make the exponent of that factor even. You will get a perfect square by multiplying by 2.

  √(2·1458) = √2916 = 54

Multiplying by 2 will give the square of 54.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.