Question

root 5 is irrational prove that​

Answer 1

here's ur ans ... hope it helps u...☺☺✌

Answer 2

$Hello !!!$

$\huge\bf\ Answer -$

➡Assume that √5 is rational

√5= where p and q are coprime

P = √5q Squaring both sides

${p}^{2} = {(\sqrt{5q} })^{2} {p}^{2} = {5q}^{2}$

-----------------(1)

Now p^2 is divisible by 5 so that by Theorem 1.2 p is also divisible by 5

So,

p = 5r (where r is any positive integer) --------(2)

Putting value of eq. (2) in (1)

we get,

${25r}^{2} = {5q}^{2}$

Now on dividing from 5 on both sides

we get, =

${5r}^{2} = {p}^{2}$

So we can conclude that p and q both have common factor 5 so they are not co-prime.

This problem erosion due to wrong assumption that √5 is rational.

So,

√5 is irrational.

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