Question

prove that under root 3 + under root 5 is an irrational no​

Answer 1

$\huge{\boxed{\mathcal{Answer:}}}$

To prove: √3+√5 is irrational

Let's assume that √3+√5 is a rational number

A Rational number can be written in the form of $\frac{p}{q}$where p,q are integers

√3+√5 = $\frac{p}{q}$

√3 = $\frac{p}{q}$-√5

By squaring both the sides,

(√3)² = ( $\frac{p}{q}$-√5)²

3 = p²/q²+√5²-2( $\frac{p}{q}$)(√5)

√5×2 $\frac{p}{q}$ = p²/q²+5-3

√5 = (p²+2q²)/q² × $\frac{q}{2p}$

√5 = (p²+2q²)/$\frac{2p}{q}$

(p²+2q²)/2pq is a rational number

√5 is a rational number.

This is contradictory to our assumption

Hence we can conclude that √3+√5 is an irrational number.