Simplify this division of square roots?
#((sqrt2)/2)/(1+(sqrt2)/2)#
3 Answers
Explanation:
The Expression
Explanation:
We will continue under the assumption that "simplifying" requires rationalizing the denominator.
First, we can remove fractions from the numerator and denominator by multiplying both by
#= sqrt(2)/(2+sqrt(2))#
Then, we rationalize the denominator by multiplying by the conjugate of the denominator, and taking advantage of the identity
#=(2sqrt(2)-sqrt(2)*sqrt(2))/(2^2-sqrt(2)^2)#
#=(2sqrt(2)-2)/(4-2)#
#=(cancel(2)(sqrt(2)-1))/cancel(2)#
#=sqrt(2)-1#
Explanation:
We will make use of the fact that
But before we can do that, we need to add the fractions in the denominator to make one fraction.
Now rationalise the denominator:
=