Question

prove that  √2+ √3 is irrational number ​

Answer 1

prove that √2 + √3 is irrational number :---

Let √2 + √3 = (a/b) is a rational no.

So,5 + 2√6 = (a2/b2) a rational no.

Since, 2√6 is an irrational no.

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Answer 2

Let √2+√3 be a rational number a.

Therefore ,

a=√2+√3

a^2=(√2+√3)^2

a^2=5+2√6

a^2/2-5/2=√6---(1)

Since a,-5 and 2 are rational numbers.

So a^2/2-5/2 is also a rational number.

But √6 is an irrational number.

Therefore ,

(1)==>Rational number = irrational number

This is not possible.

So our assumption is false.

So √2+√3 is an irrational number.