Chapter 6.5, Problem 32WE

To determine

The real solution for the equation $\sqrt{n+6}-\sqrt{n}=\sqrt{6}$ if not say so.

Answer to Problem 32WE

The solution for the equation is $\left(n\right)$ equal to $0$ .

Explanation of Solution

Given information: The given equation is,

  $\sqrt{n+6}-\sqrt{n}=\sqrt{6}\mathrm{......}\left(1\right)$

Calculation: Simplify (1),

  $\begin{array}{c}\sqrt{n+6}-\sqrt{n}=\sqrt{6}\mathrm{......}\left(\text{Given}\right)\\ \sqrt{n+6}=\sqrt{6}+\sqrt{n}\\ n+6=6+n+2\sqrt{6n}\mathrm{......}\left(\text{Squared}\right)\\ \text{or, }2\sqrt{6n}=0\\ 24n=\mathrm{0......}\left(\text{Squared}\right)\\ n=0\end{array}$