Question

Prove that root 2 +root 3 is irrational​

Answer 1

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Suppose √2 + √3 is a rational number

∴ √2 + √3 = a/b ( where a and b are integers )

Now,

Squaring both the sides

(√2 + √3)² = (a/b)²

Now,

using identity (a + b)² = a² + 2ab + b²

(√2)² + 2 (√2) (√3) + (√3)² = a²/b²

2 + 2√6 + 3 = a²/b²

5 + 2√6 = a²/b²

2√6 = a²/b² - 5/1

2√6 = a² -5b²/b²

√6 = a² - 5b²/2b²

Here,

a² - 5b²/2b² is rational as a and b are integers

∴ √6 is also Rational

But actually √6 is irrational .This contradiction has arisen due to our incorrect assumption that √2 + √3 is Rational.

So, we can conclude that √2 + √3 is irrational.

Answer 2

Answer:

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