Q. 332 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{r}+6=\sqrt{r+8}$

Step-by-Step Solution

Answer

The given equation has no solution.

Step 1. Given information.

The given equation is:

$\sqrt{r}+6=\sqrt{r+8}$

Step 2. Simplify the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{r}+6{)}^2& =& (\sqrt{r+8}{)}^2\\ (\sqrt{r}{)}^2+2(\sqrt{r}\left)\right(6)+(6{)}^2& =& r+8\\ r+12\sqrt{r}+36-r-8& =& 0\\ 12\sqrt{r}+28& =& 0\end{array}$

Step 3. Solve the equation.

Isolate the variable.

$\begin{array}{rcl}12\sqrt{r}& =& -28\\ \sqrt{r}& =& -\frac{28}{12}\\ \sqrt{r}& =& -\frac{7}{3}\end{array}$

For all real value of $x,\sqrt{x}\ge 0$.

In other words, a radical value cannot be equal to a negative value.

So, $\sqrt{r}\ne -\frac{7}{3}$ for any real value of $r$.

Step 4. Conclusion.

The given equation has no solution.