# Math Help - prove sqrt(3) + sqrt (5) is an irrational number

1. ## prove sqrt(3) + sqrt (5) is an irrational number

Given that sqrt(15) is an irrational number, prove that sqrt(3) + sqrt (5) is an irrational number.

Please teach me how to solve this question. Thank you very much.

2. Originally Posted by beta12
Given that sqrt(15) is an irrational number, prove that sqrt(3) + sqrt (5) is an irrational number.

Please teach me how to solve this question. Thank you very much.
Suppose sqrt(3)+sqrt(5) is rational, then:

(sqrt(3)+sqrt(5))^2=3+2sqrt(15)+5=8+2sqrt(15)

is rational, which implies that sqrt(15) is rational - a contradiction.

Hence sqrt(3)+sqrt)5) is irrational.

RonL

3. Hi Captainblack,

Thank you very much.