Question

prove that √3+√2 is irrational​

Answer 1

Answer:

3.146

Step-by-step explanation:

=√3+√2

=1.732+1.414

=3.146

Answer 2

Step-by-step explanation:

let us assume that √3+√2 is rational. Therefore √3+√2=p/q where q is not equal to 0; p and q are integers; (p,q)=1

So, we have

√3+√2=p/q

square both sides

(√3+√2)² = (p/q)²

(√3)² +(√2)² +2(√3)(√2) = (p/q)²

3 + 2 + 2√6 = p²/q²

5+ 2√6 = p²/q²

2√6 = {p²/q² - 5}

√6 = 1/2 {p²/q² - 5}. -(i)

We know that √6 is irrational.

But eq. (i) states that irrational = rational, which isn't true.

Hence, our assumption is wrong.

So √3+√2 is irrational.