Question

prove that is an irrational number
$\sqrt{3}$
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Answer 1

Hey mate here is your answer...

Suppose, √3 is rational number

So, take two integers a and b.

Such that, √3= a/b and suppose a and b are co-prime.

Now, squaring on both sides.

(√3)^2 = a^2/ b^2

3 = a^2 / b^2

3b^2 = a^ 2...............(1)

So, a is divisible by 3.

Now, suppose, a = 3k

Now, squaring on both sides.

a^2 = 9k^2...............(2)

Compare eq^n (1) and (2).

3b^2= 9k^2

= 9k^2 / 3b^2

b^2= 9k^2

So, b is also divisible by 3.

But a and b are co-prime.

So, our assumption is wrong.

Therefore, √3 is irrational.

Hope it help you... So, Plzz mark my ans as brainliest answer....