Question

Prove that
$( \sqrt{2 + \sqrt{3} } )is \: irrational$
​

Answer 1

Correct Question

Prove that ,√2-√3 is irrational number

$\bold\green{\underline{:Let*}}$

Assume that , √2-√3 is a rational number

• As we know that a rational number is represented
• in the form of p/q where p and q is interger.

⟹√2-√3=p/q

• here , squaring on both sides

⟹(√2-√3)²=(p/q)²

⟹√4-2*√2*√3+√9=p²/q²

⟹2-2√6+3=p²/q²

⟹1-2√6=p²/q²

⟹-2√6=p²/q²-1

Here, p²/q²-1 is a rational number and -2√6 is a irrational

number.

Since, a rational number can't be equal to the

irrational number.our assumption is wrong.

Hence,

$\bold\orange{\sqrt{2}-\sqrt{3}\:is\:a\: irrational\: number}$