Question

Let √3+√5 be rational then a/b equal to

Answer 1

Let us assume √3 + √5 is

a rational number.

√3+√5 = a/b ,

where a, b are integers and

b≠0.

On Squaring both sides of

the equation, we get

(√3+√5)² = (a/b)²

=> 3+5+2×√3×√5 = a²/b²

=> 8+2√15 = a²/b²

=> 2√15 = (a²/b²)-8

=> √15 = (a²-8b²)/2b²

Since a,b are integers , (a²-8b²)/2b² is rational , and

so √15 is rational.

But this contradicts the fact

that √15 is irrational.

So, we conclude that (√3+√5)

is irrational.

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