Question

prove that root 3 + 5 is irrational number​

Answer 1

Answer:

✓3+5 will be ✓7 and ✓7 is a irrational number as any square root that is not the square root of a perfect square is irrational .

Answer 2

Answer:

Let √3+√5 be a rational number.

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

√3+√5=p/q.

√3=p/q -√5.

squaring on both sides,

(√3)²= (p/q-√5)²

3=p²/q² + √5-2(p/q) (√5)

√5×2 p/q= p²/q²+5-3

√5= (p²+2q²)/q²×q/2q

√5= (p²+2q²)/2pq

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

Then √5 is also a rational number.

But this contradicts the fact that √5 is an irrational number.

So, our supposition is false.

Therefore, √3+√5 is an irrational number.