1.

Prove that (√3 + √5) is irrational.

Answer»

Let us assume that √3 + √5 is rational

On squaring, we get

(√3 + √5)2 is rational

3 + 2√3 x √5 + 5 is rational

8 + 2√15 is rational

Subtract 8 from above result, considering 8 is a rational number.

As we know, Difference of two rational numbers is a rational.

8 + 2√15 – 8 is rational

2√15 is rational

Which is only possible if 2 is rational and √15 is rational.

The fact is √15 is not a rational number.

Our assumption is wrong, and

(√3 + √5) is irrational.



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