Question

prove that root 3plus 4 root 5 is irrational​

Answer 1

Answer:

Let √3+√5 be a rational number. A rational number can be written in the form of p/q where p,q are integers.Therefore, √3+√5 is an irrational number

Answer 2

⇒ Let √3+√5 be a rational number.

⇒ A rational number can be written in the form of p/q where p,q are integers.

⇒√3+√5 = p/q

√3 = p/q-√5

⇒Squaring on both sides,

(√3)² = (p/q-√5)²

3 = p²/q²+√5²-2(p/q)(√5)

√5×2p/q = p²/q²+5-3

√5 = (p²+2q²)/q² × q/2p

√5 = (p²+2q²)/2pq

Therefore, √3+√5 is an irrational number.