What is the square root of 125/2?

2 Answers

It is #sqrt(125/2)=sqrt(5^3/2)=5*sqrt5/sqrt2#

Sep 21, 2015

Answer:

#(5sqrt10)/2#

Explanation:

Start by factoring 125.
#sqrt(125/2)#
#=sqrt((5*5*5)/2)#
#=sqrt((5^3)/2)#

You can already see here that you can bring 5 out.
#sqrt((5^3)/2)#
#=5sqrt(5/2)#

You can rewrite this as:
#(5sqrt5)/sqrt2#

We now need to rationalize this. We can do that by multiplying both the numerator and denominator by a radical that will eliminate the radical in the denominator. In this case, that radical is #sqrt2#.
#(5sqrt5)/sqrt2#
#=(5sqrt5)/sqrt2(sqrt2/sqrt2)#
#=(5sqrt5*sqrt2)/2#
#=(5sqrt10)/2#

You won't be able to simplify it any further. :)