Question

PROOF THAT ROOT 3 IS RATIONAL NUMBER?​

Answer 1

Answer:

Here is your answer:

Step-by-step explanation:

The root of 3 is irrational. Specifically, it cannot be written as the ratio of two given numbers or be written as a simple fraction. The value of pi is a good example of an irrational number. Also note that each and every whole number is a rational number.

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Answer 2

Hey mate.

Here your answer.....

Let us assume on the contrary that root 3 is a irrational number.

Then there positive integers a and b

Such that....

Root 3= a/b...where a and b are coprime...

Now,

Root 3 = a/b

3 = a^2/b^2

3b^2 = a^2

b^2 = 3/a^2

b= 3/a .............. Eq 1

>>>>> a= 3c for some integer c

a^2 = 9c^2

3b^2 =9c^2

b^2 = 3c^2

c^2 = 3/b^2

c= 3/b .......................... Eq 2

From 1 and 2 we observed that a and b have at least 3 as a common factor but this contradict the fact that a and b are coprime.

This means that our assumption is not correct.

Hence, root 3 is an irrational number...

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