How do you simplify #(sqrt5+sqrt2)/sqrt10#?

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Answer 1 · 2016-09-07T16:48:15

#(sqrt5+sqrt2)/sqrt10#

= #sqrt2/2+sqrt5/5#

To simplify #(sqrt5+sqrt2)/sqrt10#, we need to rationalize denominator.

As it is #sqrt10#, #(sqrt5+sqrt2)/sqrt10# can be rationalized by multiplying numerator and denominator by #sqrt10#.

Hence #(sqrt5+sqrt2)/sqrt10#

= #(sqrt10(sqrt5+sqrt2))/(sqrt10)^2#

= #(sqrt50+sqrt20)/10#

= #(sqrt(2×5×5)+sqrt(2×2×5))/10#

= #(5sqrt2+2sqrt5)/10#

= #sqrt2/2+sqrt5/5#