Question

proof the root 2 is irrational number​

Answer 1

Step-by-step explanation:

Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!

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Answer 2

Proof by contradiction:

Assume that root2 is rational

So, it can be expressed as a/b such that a and b are integers, b is not equal to 0 and HCF of a and b is 1. ------------(v)

root 2 = a/b

root 2 * b = a

2b^2 = a^2            ---------(i)

By (i) we can say that a^2 is divisible by 2

therefore, a is divisible by 2 ----------------(iii)

Hence, a = 2c (c is any integer)

root 2*b = 2c

2b^2 = 2c^2              ---------(ii)

By (ii) we can say that b^2 is divisible by 2

therefore, b is divisible by 2       --------------(iv)

Ststements (iii) and (iv) contradict the statement (v)

Hence, root 2 is an irrational number.

You can apply this same logic for other proffs too just by replacing root2 in these steps.

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