Question

prove prove root 3 + root 5 is irrational ​

Answer 1

this is your answer,...........

Answer 2

ANSWER:

$( \sqrt{5} + \sqrt{3} ) ^{2 } = {x}^{2} \\ 5 + 2 \sqrt{15} + 3 = {x }^{2} \\ 2 \sqrt{15} + 8 = {x}^{2} \\ 2 \sqrt{15} = {x}^{2} - 8 \\ \sqrt{15} = \frac{ {x }^{2} - 8}{2}$

As x is rational number.

$\frac{ {x}^{2} - 8}{2}$Is also rational number.

But $\sqrt{15}$Is a irrational number.

We get rational number = Irrational number

Which is a contradiction.

Our assumption x is rational is wrong.

$\sqrt{5} + \sqrt{3}$Is irrational number.

I HOPE IT HELPS YOU.

MARK ME AS BRAINLIEST.

FOLLOW ME.

LOVE YOU.