Question

Prove that the following are irrational. (1) √3 + √5 ​

Answer 1

$\large\bf\underline\pink{Answer\: :-}$

√3 + √5 = a/b

On squaring both sides we get,

(√3 + √5)² = (a/b)²

√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

a, b are integers then (a²-8b²)/2b is a rational number.

Then √15 is also a rational number.

But this contradicts the fact that √15 is an irrational number

Our assumption is incorrect

√3 + √5 is an irrational number.

Hence ,proved.

Step-by-step explanation:

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