Question

prove √5 is irrational
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Answer 1

Let √5 be a rational number.

then it must be in form of

p and q

where, =0 ( p and q are co-prime)

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

$\sqrt{5} \times q = p$

Squqring on both sides

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

p² is divisible by 5

p = 5c

Suaring on both sides,

p 2 =25c 2

Put p 2 in eqn.(1)

5q 2 = 25 (c) 2

q 2 =5c2

So, q is divisible by 5.

So.

Thus p and q have a common factor of 5

So √5 is irrational