Question

prove that root 3 is a irrational​

Answer 1

Answer:

Rational numbers are all positive and negative integars and zero....

All numbers which are not written in p upon q and q is not equal to zero and their decimal extention is not terminating and non reapting.....

so read defination of this chapter carefully ...

hope it help u

Answer 2

Answer:

Hey Mate Here Is Your Answer

Step-by-step explanation:

We have to prove that √3 is a irrational number

Let us assume that √3 is a rational number

Hence it can be written in the form of a/b

where a & b (bis not equal to 0) are co prime (no factor other than 1)

Hence √3= a/b

√3b=a

squaring both sides

(√3b)^2= a^2

3b^2= a^2

a^2/3= b^2

Hence 3 devides a^2

By Theorem- if p is prime number and p divides a^2 then p divides a where p is a positive number.

So 3 shall divide a also

Hence we can say

a/3= c where c is some integer

So a = 3c

Now we now that

3b^2= a^2.

Putting a= 3c

3b^2= 3c^2

3b^ = 9c^2

b^2 = 3c^2

Hence 3 divides b^2.

so 3 divides b also

Hence 3 is factor of a &b and a and b have factor 3 therefore a and b are not co prime number

Hence our assumption is wrong

therefore by contradiction

Thank You☺️

√3 is a irrational number