Question

how to prove is irrational
$\sqrt{5}$
​

Answer 1

Because root 5 = 2.236........

It is proved by long division method

Hope it helps u

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Answer 2

$\huge \pink{ \overbrace{ \purple{ \underbrace{ \blue{ \mathbf{Answer}}}}}}$

let √5 be rational

so,

$\sqrt{5} = \frac{a}{b}$

squaring on both sides,

${5b}^{2} = {a}^{2}......(.i)$

5 divides a

${a}^{2}$

5 divides a also.

let a =5c for some intiger c.

putting a =5c in (i)

$5b {}^{2} = 25c {}^{2} \\ = > b {}^{2} = 5c {}^{2}$

5 divides b square.

5 also divides b also.

Thus,

5 is a common factor of a and b .

but this contradiction is arissen because of our wrong assumption.

so √5 is irrational.