Question

express that √3-√2 is an irrational number

Answer 1

Any number subtracted from or added to an irrational number is always an irrational number.

Example: a - b

Here if b is an irrational number and a is a rational number then the end result a - b is also irrational.

Answer 2

Hi friend!!

Let √3 - √2 is a rational number.

A rational number can be written in the form of p/q.

√3 - √2 = p/q

Squaring on both sides,

(√3-√2)² = (p/q)²

√3²+√2²-2(√3)(√2) = p²/q²

3+2-2√6 = p²/q²

5-2√6 = p²/q²

2√6 = 5 - p²/q²

2√6 = (5q²-p²)/q²

√6 = (5q²-p²)/2q

p,q are integers then (5q²-p²)/2q is a rational number.

Then √6 is also a rational number.

But this contradicts the fact that √6 is an irrational number.

So,our supposition is false.

Therefore,√3-√2 is an irrational number.

Hope it helps