Q. 9.2 - Intermediate Algebra

Question

Solve $y^2-27=0$

Step-by-Step Solution

Answer

The solutions of the quadratic equation: $y=3\sqrt{3}, y=-3\sqrt{3}$ 

Step 1. Given information

Consider the quadratic equation 

$y^2-27=0$

The objective is to solve the quadratic equation by using square root property.

If $x^2=k$, then $x=\pm \sqrt{k}$

Isolate the quadratic term and make its coefficient one. Add 27 both sides to get $y^2$ by itself.

$$\begin{gathered} y^2-27=0 \\ y^2=27 \end{gathered}$$

Step 2. Use square root property.

Remember to write the $\pm$symbol.

$y=\pm \sqrt{27}$

Step 3. Simplify the radical.

Rewrite to show two solutions. 

$$\begin{gathered} y=\pm \sqrt{9}·\sqrt{3} \\ y=\pm 3\sqrt{3} \\ y=3\sqrt{3}, -3\sqrt{3} \end{gathered}$$

Step 4. Check the solutions.

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

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

And,

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