Question

Prove that √3 - √2 is irrational
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Answer 1

Hope this wil help you .

Step-by-step explanation:

Answer 2

AnswEr:

Let us assume that√3 -√2 is rational number.

So, it can be written in the form of P/Q

=> √3 - √2 = p/q

Squaring 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)/2q²

p & q are integers and (5q² -p²)/2q² is rational number.

But √6 is irrational number

So, this contradicts that √6 is irrational number.

Our assumption is incorrect.

√3 -√2 is irrational number

Hence Proved