Question

Solve$y^2-27=0$.

Short answer

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

Step-by-step solution

Given Information     

The Given equation is $y^2-27=0$.

Isolate the quadratic term and makes its coefficient one.     

$y^2=27$

 Use the square root property.     

$y=\pm \sqrt{27}$

Factor the radicand.

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

Check the solutions.   

Substitute $y=3\sqrt{3}$

$$\begin{gathered} y^2-27=0 \\ {\left(3\sqrt{3}\right)}^2-27\stackrel{?}{=}0 \\ 27-27\stackrel{?}{=}0 \\ 0=0True \end{gathered}$$

Substitute $y=-3\sqrt{3}$.

$$\begin{gathered} y^2-27=0 \\ {\left(-3\sqrt{3}\right)}^2-27\stackrel{?}{=}0 \\ 27-27\stackrel{?}{=}0 \\ 0=0True \end{gathered}$$

Thus, the solutions are$y=\pm 3\sqrt{3}$.