Question

shw that 5-√3 is irrational​

Answer 1

Step-by-step explanation:

please mark it as brainlist

Answer 2

let us assume that 5 - √3 is rational number

So, 5 - √3 can be written in the form of a/b

Where a & b ( b ≠ 0) are co - primes (No common factor other than 1)

Hence, 5 -√3 = a/b

=> -√3 = a/b -5

=> -√3 = a -5b/b

=> -√3 = a - 5b /b

=> √3 = -(a - 5b)/b

Here √3 is irrational

But -(a -5b)/b is rational number

Since Rational ≠ Irrational

This is a Contradiction

∴ Our assumption is incorrect

=> 5 - √3 is irrational number

Hence Proved