Question

Prove that √3+√5 is an irrational number:​

Answer 1

Answer:

the sum of two irrational numbers are always irrational

Step-by-step explanation:

as in

$\sqrt{3} + \sqrt{5}$

both are irrational

therefore there sum will alsi be irrational

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Answer 2

Answer:

HERE IS YOUR ANSWER

Step-by-step explanation:

Let √3 + √5 be a rational number , say r

then √3 + √5 = r

On squaring both sides,

(√3 + √5)2 = r2

3 + 2 √15 + 5 = r2

8 + 2 √15 = r2

2 √15 = r2 - 8

√15 = (r2 - 8) / 2

Now (r2 - 8) / 2 is a rational number and √15 is an irrational number .

Since a rational number cannot be equal to an irrational number . Our assumption that √3 + √5 is rational wrong .

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