Question

show that (root3+root5) is an irrational​

Answer 1

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Answer 2

Let us assume (√3+√5) is a

rational number.

Let (√3+√5) = a/b

Where , a, b are integers , b≠0

√3 = a/b - √5

Squaring on both sides

(√3)² = (a/b-√5)²

=> 3 = a²/b² + 5 - 2√5a/b

=> 2√5a/b = a²/b² +2

=> 2√5a/b = ( a²+2b²)/b²

=> 2√5a = (a²+2b²)/b

=> √5 = (a²+2b²)/2ab

Since , a,b are integers ,

(a²+2b²)/2ab is rational , and

so , √5 is rational.

This contradicts the fact that

√5 is irrational.

Hence √3+√5 is irrational.

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