Question

prove that root 3 is an irrational no.

Answer 1

Let the root 3 be rational

root 3 can be written in form of p upon q

where a and b are coprime

√3 = a/b

a = b√3..............eq.1

b = a / √3

squaring both sides

b^2 = a^2 / 3

3 divides a^2

3 also divides a

a / 3 = c

a = 3c

from eq.1

b√3 = 3c

squaring both sides

3b^2 = 9c^2

b^2 = 3 c^2

c^2 = b^2/3

3 divides b^2

3 divides b

3 divides a and b both

but a and b are co prime no.

This contradiction arises due to our wrong assumption. So √2 is irrational no.

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