Question

prove that √3 is an irrational number ​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

let √ 3 be rational number ?

then √3 = a/b where a and b are co primes also b ≠ 0

√3= a/b

√3b= a

on squring both sides

[√3b]²= a²

3b²= a²

from here we can say that 3 divides a

let a = 3k

on squring both sides

a²= (3k)²

also a²= 3b²

so 3b²= 9k²

b²= 3k²

from here 3 also divides b²

so a and b has at least 3 as there comman factor hence they are not coprimes

therefore our assumption is wrong √3 is ≠ a/b

thus √ 3 is irrational

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