Question

prove that,√3 is irrational number with approval answer​

Answer 1

Step-by-step explanation:

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Answer 2

We know every rational number can be expressed in the form p/q, where p & q are integers and q ≠ 0.

Let √3 be a rational number.

√3 = p/q (p & q are co-primes)

Squaring both sides

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

$3= \frac{ {p}^{2} }{ {q}^{2} }$

$3{q}^{2} = {p}^{2}$

3 divides p²

i.e. 3 divides p

Let, p = 3m

p² = 9m²

3q² = 9m²

q² = 3m²

3 divides q²

i.e 3 divides q

p & q have already two common factors. But this contradicts the fact that p & q are co-primes.

Thus, √3 is not a rational number.

Therefore, √3 is a irrational number.