Question

Solve the quadratic equation using square root property.

$a^2-18=0$

Short answer

The solutions are$a=\pm 3\sqrt{2}$.

Step-by-step solution

Given Information  

The Given equation is$a^2-18=0$.

Isolate the quadratic term and makes its coefficient one.  

$$\begin{gathered} a^2-18=0 \\ {a}^2=18 \end{gathered}$$

 Use the square root property.   

$a=\pm \sqrt{18}$

Factor the radicand.

$$\begin{gathered} a=\pm \sqrt{2\times 3\times 3} \\ a=\pm 3\sqrt{2} \end{gathered}$$

Check the solutions.

Substitute $a=3\sqrt{2}$

$$\begin{gathered} a^2-18=0 \\ {\left(3\sqrt{2}\right)}^2-18\stackrel{?}{=}0 \\ 18-18\stackrel{?}{=}0 \\ 0=0True \end{gathered}$$

Substitute $a=-3\sqrt{2}$

$$\begin{gathered} a^2-18=0 \\ {\left(-3\sqrt{2}\right)}^2-18\stackrel{?}{=}0 \\ 18-18\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Thus, the solutions are$a=\pm 3\sqrt{2}$