# Prove that the real number√ 2 + √5 is not rational.l​

Prove that the real number

2 +
√5 is not rational.l​

### 2 thoughts on “Prove that the real number<br />√<br /> 2 +<br /> √5 is not rational.l​”

1. √2 + √5

√2 value is 1.414..

√5 value is 2.236…

1.414..+2.236..

= 3.65..

it has a repeating decimal

°°°° there fore it’s irrational number

### if it helps you drop a thanks

Step-by-step explanation:

Prove that (root 2 + root 5 ) is irrational

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.