# What is the smallest counting (n) number that would make 756n a perfect square?

Jul 6, 2015

756 xx color(green)(21) = color(blue)(15876

$\sqrt{15876} = 126$

#### Explanation:

$756 = \left(2 .2\right) . \left(3 .3\right) . \left(3\right) . \left(7\right)$

As we can observe $756$ is short of the number
color(blue)(3 . 7 =21 for perfect square.

So, color(blue)(756 . 21 = 15876

$15876$ is a perfect square.

756 . 21 = color(blue)(15876

$\sqrt{15876} = 126$