Q. 335 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{a+5}-\sqrt{a}=1$

Step-by-Step Solution

Answer

The solution of the given equation is $a=4$.

Step 1. Given information.

The given equation is:

$\sqrt{a+5}-\sqrt{a}=1$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{a+5}=1+\sqrt{a}$

Take square on both sides.

$\begin{array}{rcl}(\sqrt{a+5}{)}^2& =& (1+\sqrt{a}{)}^2\\ a+5& =& (1{)}^2+2(1\left)\right(\sqrt{a})+(\sqrt{a}{)}^2\\ a+5& =& 1+2\sqrt{a}+a\\ 5-1& =& 2\sqrt{a}+a-a\\ 4& =& 2\sqrt{a}\end{array}$

Step 3. Solve the equation.

Divide both sides by 2.

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

Step 4. Conclusion.

The solution of the given equation is $a=4$.