Prove that (√2 + √3) is irrational.

Question

KnowledgeBoat · Accepted Answer

Let us assume is a rational number. Let, Squaring on both sides, we get : Here, x is rational, ∴ x2 is rational .........(1) ⇒ x2 - 5 is rational (Difference between two rational numbers is always rational) So, is rational (Dividing two rational numbers results in a rational number) But is irrational, is irrational Thus, x2 - 5 is irrational and so x2 is irrational ........(2) (1) and (2) do not match with each other. ∴ We arrive at a contradiction. So, our assumption that is a rational number is wrong. ∴ is irrational. Hence, proved that is an irrational number.

Mathematics

Prove that (√2 + √3) is irrational.

Rational Irrational Nos

Related Questions

Write down the examples of 4 distinct irrational numbers.