Question

prove that 5+7√3 is an irrational number​

Answer 1

Answer:

let be assume that 5+7√3 is a rational number.

let be assume that 5+7√3 is a rational number.therefore, it can be written in the form of p/q

let be assume that 5+7√3 is a rational number.therefore, it can be written in the form of p/q5+7√3 = p/q

let be assume that 5+7√3 is a rational number.therefore, it can be written in the form of p/q5+7√3 = p/q7√3 = p-5q/q

let be assume that 5+7√3 is a rational number.therefore, it can be written in the form of p/q5+7√3 = p/q7√3 = p-5q/q√3 = p-5q/7q

let be assume that 5+7√3 is a rational number.therefore, it can be written in the form of p/q5+7√3 = p/q7√3 = p-5q/q√3 = p-5q/7qp-5q/7q is a rational number therefore √3 is also a rational number but it is contradict that √3 is an irrational number therefore our assumption is wrong an 5+7√3 is an irrational number.q

Answer 2

Step-by-step explanation:

by contradictory method

I assumed that it is a rational number

we know that a rational number can be written in the form of p/q but in conclusion we observed that ^3 as rational

so our assumption is wrong

therefore the given number is irrational