Question

show that 5-√3 is irrational​

Answer 1

Answer:

Here root 3 is irrational and 5 is rational so,subtraction between rational and irrational = irrational.

Answer 2

Step-by-step explanation:

Suppose 5-√3 is rational .

Every rational no. can be expressed in the form of p/q , where p,q are co-prime integers and q ≠ 0 .

So suppose 5-√3 = $\frac{p}{q}$ for some p,q .

Then 5 - $\frac{p}{q}$ = √3

=> $\frac{5q - p}{q}$ = √3

We know √3 is irrational ,  so $\frac{5q - p}{q}$ also has to be irrational .

But $\frac{5q - p}{q}$ is on the form of p/q , so it is rational , which is a contradiction .

So 5√3 is irrational