Q. 331 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{a}+2=\sqrt{a+4}$

Step-by-Step Solution

Answer

The solution of the given equation is $a=0$.

Step 1. Given information.

The given equation is:

$\sqrt{a}+2=\sqrt{a+4}$

Step 2. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{a}+2{)}^2& =& (\sqrt{a+4}{)}^2\\ (\sqrt{a}{)}^2+2(\sqrt{a}\left)\right(2)+(2{)}^2& =& a+4\\ a+4\sqrt{a}+4& =& a+4\end{array}$

Isolate variable terms.

$\begin{array}{rcl}a+4\sqrt{a}-a& =& 4-4\\ 4\sqrt{a}& =& 0\\ \sqrt{a}& =& 0\\ a& =& 0\end{array}$

Step 3. Conclusion.

The solution of the given equation is $a=0$.