Question

Prove that 2 route 2- route 5 is irrational

Answer 1

Let 2√2-√5 be a rational no.
2√2-√5 = p/q where p and q are co prime integers and q not = to 0
2√2 = p/q + √5
√2 = p/q +√5 /2
Here , LHS is irrational but RHS is rational which is contradiction to our supposition .
So , our assumption is wrong ...
Given , ..... is irrational
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