How do you simplify #sqrt (18) / (sqrt (8) - sqrt (2))#?

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Answer 1 · 2018-05-16T17:48:38

Simplify each radical individually, and then work with the fraction as a whole. You will find that the simplified version is #3#

First, we'll simplify the numerator:

#sqrt(18)=sqrt(9xx2)#

#sqrt(9xx2)=sqrt(9)xxsqrt(2)#

#sqrt(9)xxsqrt(2)=3xxsqrt(2)=color(orange)(3sqrt(2)#

Now the expression can be written as:

#color(orange)(3sqrt(2))/(sqrt(8)-sqrt(2))#

Next, we'll simplify the denominator:

#sqrt(8)-sqrt(2)=sqrt(4xx2)-sqrt(2)#

#sqrt(4xx2)-sqrt(2)=sqrt(4)xxsqrt(2)-sqrt(2)#

#sqrt(4)xxsqrt(2)-sqrt(2)=2xxsqrt(2)-sqrt(2)=2sqrt(2)-sqrt(2)#

#2sqrt(2)-sqrt(2)=(2-1)sqrt(2)=color(blue)(sqrt(2))#

Re-write the expression again:

#color(orange)(3sqrt(2))/color(blue)sqrt(2)#

Finally, we can simplify the fraction:

#(3cancel(sqrt(2)))/cancel(sqrt(2))=color(green)(3)#