What is the simplified form of square root of 10 - square root of 5 over square root of 10 + square root of 5?

1 Answer
Alan P.
Sep 12, 2015

(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)=3-2sqrt(2)

Explanation:

(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)
color(white)("XXX")=cancel(sqrt(5))/cancel(sqrt(5))*(sqrt(2)-1)/(sqrt(2)+1)

color(white)("XXX")=(sqrt(2)-1)/(sqrt(2)+1)*(sqrt(2)-1)/(sqrt(2)-1)

color(white)("XXX")=(sqrt(2)-1)^2/((sqrt(2)^2-1^2)

color(white)("XXX")=(2-2sqrt2+1)/(2-1)

color(white)("XXX")=3-2sqrt(2)

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