Question

Show that √5+ √3 is an irrational number.​

Answer 1

Hi
Here:
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.

Answer 2

Hey,

　

Question :-

Prove that √5 + √3 is an irrational number

　

Solution :-

√5 = Irrational

√3 = Irrational

Irrational + Irrational = Irrational

So, √5 + √3 is an Irrational number

　

Further Information :-

1. Irrational + Irrational = Irrational

2. Irrational - Irrational = Irrational

3. Irrational + Rational = Irrational

4. Irrational - Rational = Irrational

5. Rational + Rational = Rational

6. Rational - Rational = Rational

7. A number with infinite decimal expansion is called irrational number

8. A number with a specific decimal expansion is called rational number

9. All natural numbers, whole numbers, integers, rational numbers, irrational number can be classified as real numbers

　

HOPE THAT HELPS :)

@MagicHeart