Question

Prove that √5 is irrational, hence show that (3 + 2√5) is an irrational number​

Answer 1

let us assume that √5 is a rational number

so, √5 = p/q where q is not equal to 0 and p and q have no common factors other than 1

on squaring both side,

5 = p²/q²

5q² = p²

q² = p²/5

p² divided by 5

p also divided by 5

Now,

put p = 5m

so, q² = (5m)²/5

q² = 25m²/5

q² = 5m²

m² = q²/5

q² divided by 5

q also divided by 5

Here, p & q have common factor as 5

so, our assumption is wrong.

Hence √5 is an irrational number!!!

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