Question

prove that
$\sqrt{3}$
is irrational....​

Answer 1

Answer:

$\sqrt{3}$

is irrational.... because

we can't get the approx Value of

$\sqrt{3}$

Answer 2

Answer:

So to prove that ✓3 is irrational we'll take the contrary

Let us assume that ✓3 is rational

Therefore, there exist some co- prime integers a and b

✓3 = p/q

3 = p^2 / q^2 [squaring both sides]

3q^2 = p^2 ........( 1 )

It means that 3 divides p^2 and also 3 divides p because each factor should appear two times for the square to exist.

where r is some integer.

p^2 = 9r^2 ...........( 2 )

From eqn (1) and (2)

3q^2 = 9r^2

q^2 = 3r^2

where q^2 is a multiple of 3 and also q is a multiple of 3

Then p, q have a common factor of 3. This runs contrary to their being co-primes. Consequently, p / q is not a rational number. This demonstrates that √3 is an irrational number.

Hope it helps!!!!

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