How do you find the square root of 5625?

2 Answers
Sep 8, 2015

Answer:

Split into prime factors, identify factors which occur in pairs, hence find: #5625 = 75^2#, so:

#sqrt(5625) = 75#

Explanation:

Start by finding prime factors of #5625#:

#2#: No: #5625# is odd.
#3#: Yes:
#color(white)(XX)5625 = 3 * 1875 = 3 * 3 * 625#
#5#: Yes:
#color(white)(XX)3 * 3 * 625 = 3 * 3 * 5 * 125 = 3 * 3 * 5 * 5 * 25#
#color(white)(XX)= 3 * 3 * 5 * 5 * 5 * 5 = (3*5*5)^2 = 75^2#

Jul 3, 2018

Answer:

#sqrt5625=75#

Explanation:

As the number ends with #25 =5^2#, 5625, therefore, is a multiplum of 25.

I also recognise that #25^2=625#, which is the last part of 5625. I would, therefore, check if 5625 is a multiplum of 625:
#5625/625=9=3^2#

Therefore #5625=3^2*25^2=75^2#

Therefore #sqrt5625=75#