Question

Prove that 2√3-√5 is an irrational number

Answer 1

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Let the 2+root3 root 5 be a rational no.

Therefore it can be written in form of p/q (q not =0 and p, q are co. Prime)

2+......=p/q

Root 3 root 5=p/q - 2

Root 3=1/root(p/q-2)

Here in lhs root 3 is irrational and in RHS all the no. Are rational....hence our supposition is wrong.. It is contradict to fact that the root3 is irrational and a rational no. Can't be equal to the irrational..

So the given no...... Is irrational.