Question

prove that ( √2 + √5 ) is irrational​

Answer 1

Answer:

√2 and √5 both are irrational numbers. it is the rule that when an irrational number interacts with a rational no. or another irrational number, the answer will always be irrational. these two numbers are in addition, so their sum will also be irrational

Answer 2

Answer: Yes,√2+√5  is irrational.

Step-by-step explanation:

Given: √2+√5

We need to prove√2+√5 is an irrational number.

Proof

Let us assume that √2+√5 is a rational number.

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.

HOPE THIS HELPED YOU....

PLS.mark me as the brainliest