Question

Hi friends
prove √2+√3 is irrational.
(proper steps are needed)

Answer 1

Hi mate here is your answer

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√6 = (a2/b2) – 5Since, 2√6 is an irrational no. and (a2/b2) – 5 is a rational no.
 So, my contradiction is wrong. So, (√2 + √3) is an irrational no.

hope it helps you

mark me as a brainleast

Answer 2

Answer:

√2 + √3 is irrational.

Step-by-step explanation:

Let us assume that √2 + √3 is rational.

Hence, √2 + √3 can be written in the form a/b{a and b are co-primes, b≠0)

⇒ √2 + √3 = a/b

On squaring both sides, we get

⇒ (√2 + √3)² = (a/b)²

⇒ 2 + 3 + 2√2 * √3 = a²/b²

⇒ 5 + 2√6 = a²/b²

⇒ 2√6 = (a²/b²) - 5

⇒ 2√6 = (a² - 5b²)/b²

⇒ √6 = (a² - 5b²)/2b²

Here, (a² - 5b²)/2b² is a rational number.

But, √6 is irrational.

Since, Rational ≠ Irrational.

This is contradiction.

∴ Our assumption is incorrect.

Hence, √2 + √3 is irrational.

Hope it helps!