How do you rationalize the denominator and simplify #sqrt(5/10)#?

1 Answer
Apr 18, 2016

Answer:

#sqrt2/2#

Explanation:

First, we can simplify what's in the big root sign:
#sqrt(5/10)=sqrt(1/2)#
And we can split the big root sign into two smaller ones:
#=sqrt1/sqrt2#
#=1/sqrt2#
Now we do something unexpected, and put another term into the equation.
#=1/sqrt2*sqrt2/sqrt2#
We can do this because #sqrt2/sqrt2# is just 1, and anything times 1 is itself. Moreover we do this because the question asks us to rationalise the denominator, asking to remove any root signs.
#=sqrt2/(sqrt2*sqrt2)#
#=sqrt2/2#