Question

Show that √12 is irrational number

Answer 1

Here's your answer with the attachment:-

Answer 2

Answer:

Step-by-step explanation:

$( \frac{m}{n} ) {}^{2 } = 12$

$( \frac{m}{2n} ) {}^{2} = 3$

$m {}^{2} = 3 \times (2n) {}^{2}$

This implies mm is even and so nn must be odd.

The problem can be reduced to:

$( \frac{p}{n} ) {}^{2} = 3$

Because n is odd, p² is odd, so p is odd.

This implies:

$4a + 1 = 3(4b + 1)$

$4a - 12b = 2$

$2a - 6b = 1$