Chapter 8.7, Problem 14WE

To determine

To show: that the $\sqrt{6}$ is irrational number.

Explanation of Solution

Given information:

The number is $\sqrt{6}$ .

Proof: since, $\sqrt{6}$ is a root of the equation $x^2-6=0$ . The only possible rational roots of this equation are $\pm 1,\pm 2\text{,}\pm 3\text{ and }\pm 6$ .

None of these eight numbers satisfies the equation.

Since, equation $x^2-6=0$ has no rational roots,

Thus, $\sqrt{6}$ is irrational.