Question

prove root 3 is an irrational number​

Answer 1

Answer:

Let root3 be a rational number where it can be written in the form a/b where a and b are integers and b is not equal to 0. Also, a and b are coprime.

Root3=a/b

Squaring both sides, we get

3=a^2/b^2

3b^2=a^2

b^2=a^2/3

Now, a^2 is divisible by 3 and 3 is prime.

Therefore, a is divisible by 3.

Now, let a=3c

b^2=3c^2

c^2=b^2/3

b^2 is divisible by 3.

Therefore, b is divisible by 3.

It contradicts the fact that a and b are coprime.

This contradiction has arisen due to our wrong assumption.

Therefore, root3 is irrational.

Hope it will help..

Mark the brainliest

Answer 2

Step-by-step explanation:

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