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

1 Answer
Jul 6, 2015

Answer:

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

#sqrt15876 = 126#

Explanation:

#756 = (2 .2) . (3 .3) .(3) .(7)#

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 #

#sqrt15876 = 126#