Q.8 - Intermediate Algebra

Question

Solve Quadratic Equations of the Form $a{x}^2=k$

Using the Square Root Property.

In the following exercises, solve each equation $3n^2=48$

Step-by-Step Solution

Answer

The solution of the quadratic equation: $n=4, n=-4$

Step 1. Given information

Consider the quadratic equation $3n^2=48$

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 3 to make its coefficient 1.  

$$\begin{gathered} \frac{3n^2}{3}=\frac{48}{3} \\ n^2=16 \end{gathered}$$

Step 2. Apply square root property

So, $n=\pm \sqrt{16}$

Simplify the radical.    

$$\begin{gathered} n=\pm \sqrt{4·4} \\ n=\pm 4 \end{gathered}$$

Rewrite to show two solutions. 

$n=4, n=-4$ 

Step 3. Check the solutions

Substitute $n=4$in the original equation

$$\begin{gathered} 3n^2=48 \\ 3{\left(4\right)}^2\stackrel{?}{=}48 \\ 3\left(16\right)\stackrel{?}{=}48 \\ 48=48 \end{gathered}$$

Substitute $n=-4$ in the original equation

$$\begin{gathered} 3n^2=48 \\ 3{(-4)}^2\stackrel{?}{=}48 \\ 3\left(16\right)\stackrel{?}{=}48 \\ 48=48 \end{gathered}$$