√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 Reply

Answer: Mark my answer as brainlist 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. Reply

√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

Answer:Mark my answer as brainlist

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.