Question

Give that √3 is irrational, prove that 5√3-2 is an irrational number?​

Answer 1

Step-by-step explanation:

Let 5√3-2 be rational number.

rational numbers are in the form of P/q.

so, 5√3-2=p/q

=> 5√3=p/q+2

=> 5√3=p+2q/q.

=> √3=P+2q/5q.

Given.that √3 is irrational number.

so, p+2q/5q is also irrational.

Therefore, our assumption is wrong that 5√3-2 is rational.

5√3-2 is an irrational number.