Question

prove that 2 root 5 is an irrational number.

Answer 1

Hey.... I think this can be ur answer!!

Let us assume that 2+root5 is rational

SO,

2+root5 = a/b

Root5 = a/b-2 =a-2b/b

But we know that root5 is irrational

So,

Our assumption was wrong

Therefore, 2+root5 is irrational

Hence proved

Hope it helps you dear ☺️☺️

Answer 2

Answer:

Step-by-step explanation:

A rational number can be written in the form of p/q where p,q are integers and q≠0

√2+√5 = p/q

On squaring both sides we get,

(√2+√5)² = (p/q)²

√2²+√5²+2(√5)(√2) = p²/q²

2+5+2√10 = p²/q²

7+2√10 = p²/q²

2√10 = p²/q² – 7

√10 = (p²-7q²)/2q

p,q are integers then (p²-7q²)/2q is a rational number.

Then √10 is also a rational number.

But this contradicts the fact that √10 is an irrational number.

Our assumption is incorrect

√2+√5 is an irrational number.

Hence proved.

mark me brianliest