Question

Prove that √3+√5 is irrational number​

Answer 1

Answer: we can take it as a/ b .

so √3+√5= a/b

now we will solve it according to the properties, on squaring it on both the sides we get.

(√3+√5) power 2 = a square/b square

√3² + √5² + 2(√5)(√3) = a²/b²

3 + 5 + 2√15 = a²/b²

8 + 2√15 = a²/b²

2√15 = a²/b² – 8

√15 = (a²- 8b²)/2b.

here, √ 15 is irrational. hope it helps u:)

Answer 2

Answer:

Step-by-step explanation:

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+√5²-2(p/q)(√5)

√5×2p/q = p²/q²+5-3

√5 = (p²+2q²)/q² × q/2p

√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.

Hope it helps!