Question

m wide.
Q.3 Find the smallest whole number by which 1458 should be
multiplied to get a number whose square root is a natural number.
Alto
2
2) 1/23​

Answer 1

By prime factorisation of 1458, we get

1458=2×3×3×3×3×3×3

Here, 3 are in pairs but 2 needs a pair to make 1458 a perfect square.

So, 1458 needs to be multiplied by 2 to make it a perfect square.

Thus, the number is 1458×2=2916

$\sqrt{2916} = \sqrt{2×2×3×3×3×3×3×3}$

=2×3×3×3

=54

Thus 2 is the required smallest whole number to make the given number a perfect square.