What is the square root of #360# divided by #640# ?

1 Answer
Apr 23, 2017

Answer:

#sqrt(360/640) = 3/4#

Explanation:

I think what you want is the simplified form of the square root of #360/640#.

If so then first note that if #a, b > 0# then:

#sqrt(a/b) = sqrt(a)/sqrt(b)#

Also, if #a >= 0# then:

#sqrt(a^2) = a#

So we find:

#sqrt(360/640) = sqrt((2^3*3^2*5)/(2^7*5)) = sqrt(3^2/2^4) = sqrt(3^2)/(sqrt((2^2)^2)) = sqrt(3^2)/sqrt(4^2) = 3/4#

Alternatively:

#sqrt(360/640) = sqrt((36*color(red)(cancel(color(black)(10))))/(64*color(red)(cancel(color(black)(10))))) = sqrt(36/64) = sqrt(36)/sqrt(64) = sqrt(6^2)/sqrt(8^2) = 6/8 = 3/4#