Question

Prove that
$\sqrt{5}$
is rational number.

​

Answer 1

[tex]Answer:

\sqrt{5} = \frac{p}{q}

5

=

q

p

Squaring on both the sides we get,

5 = \frac{ {p}^{2} }{ {q}^{2} } 5=

q

2

p

2

5 {q}^{2} = {p}^{2} 5q

2

=p

2

p = 5kp=5k

p is divisible by 5

k is positive integer

Again squaring on both the sides

{p}^{2} = 25 {k}^{2} p

2

=25k

2

{q}^{2} = \frac{ {25k}^{2} }{5} q

2

=

5

25k

2

{q}^{2} = 5 {k}^{2} q

2

=5k

2

q is divisible by 5

We can say that p and q have a common factor which is 5. p and q are co- prime.

\sqrt{5} \: is \: an \: irrational \: number

5

is \: a \: rationalnumber

☆Solution☆