What is the simplest form of the radical expression of (sqrt2+sqrt5)/(sqrt2-sqrt5)?

2 Answers
Gió
Apr 23, 2015

Multiply and divide by sqrt(2)+sqrt(5) to get:
[sqrt(2)+sqrt(5)]^2/(2-5)=-1/3[2+2sqrt(10)+5]=-1/3[7+2sqrt(10)]

Elijah T.
Feb 5, 2017

Conjugate

Explanation:

Just to add on to the other answers,

We decided to multiply the top and the bottom by sqrt(2)+sqrt(5) because this is the conjugate of the denominator, sqrt(2)-sqrt(5).

A conjugate is an expression in which the sign in the middle is reversed. If (A+B) is the denominator, then (A-B) would be the conjugate expression.

When simplifying square roots in the denominators, try multiplying the top and bottom by the conjugate. It will get rid of the square root, because (A+B)(A-B) = A^2-B^2, meaning you will be left with the numbers in the denominator squared.

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