Question

prove that root 3 is an irrational number​

Answer 1

Answer:

because it is recurring

Answer 2

Answer:

Let us assume that √3 is rational.

That is, √3 = a/b, where a and b are co-prime integers and b ≠ 0.

Squaring on both sides, we get,

3 = a²/b²

3b² = a² ----- 1

Therefore, 3 divides a²,

Therefore, 3 divides a ----- 2

Therefore, a = 3(c) for some integer 'c'. -----3

3 in 1,

3b² = (3c)²

3b² = 9c²

b² = 3c²

Therefore, 3 divides b²,

Therefore, 3 divides b ------- 4

Therefore, 2 and 4 implies,

3 is a factor common to both, a and b.

This contradicts the fact that a and b are co-prime integers.

Therefore, √3 is irrational.

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