Question

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation$\frac{5}{3}{y}^2=60$.

Short answer

The solution of the quadratic equation:$y=6,y=-6$

Step-by-step solution

Step 1. Given information

Consider the quadratic equation $\frac{5}{3}{y}^2=60$

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

If $x^2=k$, then $x=\pm \sqrt{k}$

The quadratic term is isolated. Divide by $\frac{3}{5}$to make its coefficient 1.

$$\begin{gathered} \frac{3}{5}\left(\frac{5}{3}{y}^2\right)=\frac{3}{5}\left(60\right) \\ {y}^2=36 \end{gathered}$$

Step 2. Apply square root property    

So, $y=\pm \sqrt{36}$

Simplify the radical.

$$\begin{gathered} y=\pm \sqrt{6·6} \\ y=\pm 6 \end{gathered}$$

Rewrite to show two solutions.

$y=6,y=-6$

Step 3. Check the solutions  

Substitute $y=6$in the original equation.

role="math" localid="1645638013278" $$\begin{gathered} \frac{5}{3}{y}^2=60 \\ \frac{5}{3}{\left(6\right)}^2\stackrel{?}{=}60 \\ \frac{5}{3}\left(36\right)\stackrel{?}{=}60 \\ 60=60 \end{gathered}$$

Substitute $y=-6$in the original equation.

$$\begin{gathered} \frac{5}{3}{y}^2=60 \\ \frac{5}{3}{(-6)}^2\stackrel{?}{=}60 \\ \frac{5}{3}\left(36\right)\stackrel{?}{=}60 \\ 60=60 \end{gathered}$$