[tex]\large{\underline{\underline{\red{\tt{\purple{\leadsto } SolutioN:-}}}}}[/tex]
Here we are asked to find the smallest number which must be multiplied to 240 to make it a perfect square .
So , lets do prime factorisation of 240 .
Here , 240 = 2 × 120 .
= 2 × 2 × 60.
= 2 × 2 × 2 × 30.
= 2 × 2 × 2 × 2 × 3 × 5 .
Hence we got 240 = 2⁴ × 3¹ × 5¹ .
Now here we can see that , in order to make a perfect square it should be multiplied by 3 × 5 = 15 in order to make power of prime factors even .
[tex]\boxed{\green{\bf{\dag Hence\: Required\: Number\:is\:15.}}}[/tex]
