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 $(sqrt5+sqrt2)/sqrt10$

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

= $(sqrt50+sqrt20)/10$

= $(sqrt(2×5×5)+sqrt(2×2×5))/10$

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

= $sqrt2/2+sqrt5/5$

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