Question

prove that root2 +root3 is irrational given that root6 is irrational

Answer 1

Step-by-step explanation:

Let √2 + √3 = (a/b) is a rational no. On squaring both sides , we get 2 + 3 + 2√6 = (a2/b2) So,5 + 2√6 = (a2/b2) a rational no. ... So, (√2 + √3) is an irrational no.

Answer 2

take root 2 and root 3 as rational

Step-by-step explanation:

root2+root3=x

squaring

2+3+2xroot2xroot3=x²

5+2xroot2xroot3=x²

5+2xroot6=x²

2xroot6=x²-5

root6=x²-5/2

so x is rational

and root 6 also

but it is given it is irrational

hejnce proved