Question

Prove that√3+√4 is an irrational number.​

Answer 1

Answer:

Lets assume that :

√3 + √4 is rational.

√3 + √4 = r , where r is rational

Squaring both sides ,we get

[√3 + √4 ]² = r²

3 + 2√12 + 4 = r²

7 + 2√12 = r²

2√12 = r² - 6

√12 = [ r² - 6] / 2

R.H.S is purely rational ,

whereas , L.H.S is irrational.

This is a contradiction.

This means that our assumption was wrong.

Hence , √3 + √4 is irrational.

Hope this helps you....