Question

Prove that √2 + √5 is irrational​

Answer 1

Answer:

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.

Step-by-step explanation:

I think this will help you

Answer 2

Question:-

• Prove that √2 + √5 is irrational.

step-by-step explaination:-

Let √2+√5 be a rational number.

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

⟶ √2+√5 = p/q

Squaring on both sides,

⟶ (√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 supposition is false.

√2+√5 is an irrational number.

Hence proved.!!