Question

Prove that √3 is irrational number​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let's assume that √3 is a rational number.

√3=a/b (where a and b are integers and b is not equal to 0, and, the common factor of a and b is only 1)

(√3) ^2 =(a/b) ^2 (squaring both sides)

3= a^2/b^2

3b^2= a^2

This shows that a^2 is divisible by 3.

This, a is also divisible by 3.

Let a= 3c

a^2 = (3c)^2

a^2 = 9c^2

3b^2= 9c^2 ( as a^2 = 3b^2)

b^2= 9c^2/3

b^2= 3c^2

This shows that b^w is divisible by 3.

Thus, b is also divisible by 3.

As both a and b are divisible by 3, their common factor is 3.

This contradicts our assumption that a/b is a rational number

Therefore a/b = √3 is an irrational number.

Hence proved.