Question

Prove that √3+√7 is an irrational number

with step by step explanation​

Answer 1

Given:-

Prove that √3 + √7 is an irrational number.

Now,

Let √3 + √7 equal to x where x is rational

number ,

→ √3 + √7 = x

→ ( √3 + √7 )² = x²

→ ( √3 )² + 2 × √3 × √7 + ( √7 )² = x²

→ 3 + 2√21 + 7 = x²

→ 10 + 2√21 = x²

→ x² - 10 = 2√21

→ x² - 10/2 = √21.

So, If x is rational number than x² is rational number as it is equal to √21 but it Contradict the fact √21 is irrational number.

• To Prove any number as irrational then the best method is to first consider it as rational number.

• Then, by Contradication method we can prove it as wrong.

• Hence, we can Prove it as Irrational number.