Question

prove that root under 3 irrational no.

Answer 1

Since (n^2+n) is an integer, the left hand side is even. ... The number isirrational ,it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it

Answer 2

Hey!

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Let assume that √3 is a rational.

Then we can find CO Prime integers a and b

(B ≠ 0)

=> √3 = a ÷ b

=> √3b = a

•Squarring both sides :-

(√3b)² = a²

3 divides a² , so 3 divides a (Theoram)

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So we can write a = 3c

Where c is some in some integer

3b² = (3c)²

= 3b² = 9c²

3 divides b² and so 3 divides b (Therom)

•A and b have a common factor 3 other than 1 which contradicts the fact that a and b are Co Prime. Thus the assumption that √3 is rational is not correct.

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Hence √3 is an irrational number


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Regards :)

Cybary

Be Brainly :)