Question

PROVE THAT ROOT 5 IS AN IRRATIONAL NUMBER

Answer 1

Hello Mate!

Let √5 be a rational number p/q where p/q is at simplest form.

√5 = p/q

5 = p² / q²

5q² = p²

Hence, 5 is factor of p.

Let m be any natural number in place of q where,

5 = p / m

5² = p² / m²

25m² = p²

25 m² = 5q²

5m² = q²

Hence 5 is factor of q.

Since 5 is factor of p and q both then it means that p/q is not in simplest form which we told earlier. This contradicts our assumption.

Hence √5 is irrational number.

Have great future ahead!

Answer 2

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are intezers.

so, √5 = p/q

    p = √5q

we know that 'p' is a rational number. so √5 q must be rational since it equals to p

but it doesnt occurs with √5 since its not an intezer

therefore, p =/= √5q

this contradicts the fact that √5 is an irrational number

hence our assumption is wrong and √5 is an irrational number.

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