How do you find the square root of 320?

1 Answer
Sep 20, 2015

Answer:

#8*sqrt5#

Explanation:

I don't know either,
so let's break it down into pieces, shall we?

We have:
#sqrt320#
The only thing that involves 32 in my mind is #4*8# or #2*16#, and so we notice that #320=2*160# or #4*80# or #16*20# or #8*40#, etc...

Let's try with #4*80#:

#sqrt320=sqrt(4*80)#
At this point, it is good to remember the rule:
#sqrt(a*b)=sqrt(a)*sqrt(b)#
so that
#sqrt320=sqrt(4*80)#
#=sqrt(4)*sqrt80#
#=2*sqrt80#

Then you see that #80=4*20#, so:

#sqrt320=2*sqrt80#
#=2*sqrt(4*20)#
#=2*sqrt(4)*sqrt(20)#
#=2*2*sqrt(20)=4*sqrt20#

Again you see that #20=4*5#, so:
#sqrt320=4*sqrt20#
#=4*sqrt(4*5)#
#=4*sqrt4*sqrt5#
#=4*2*sqrt5#
#=8*sqrt5#