Question

Solve by using the square root property. Express the solution set in exact simplest form.(v+9)^2= 20

Answer 1

The square root property states the following:

`\begin{gathered} \text{If }x^2=c\text{ and }c>0 \\ \text{ There are 2 real solutions} \\ x_1=\sqrt[]{c}\text{ and }x_2=-\sqrt[]{c} \end{gathered}`

To solve the equation, we apply square root to both sides.

`\begin{gathered} (v+9)^2=20 \\ \sqrt[]{(v+9)^2}=\sqrt[]{20} \\ v+9=\sqrt[]{4\cdot5} \\ v+9=\sqrt[]{4}\cdot\sqrt[]{5} \\ v+9=2\sqrt[]{5} \end{gathered}`

Now, we apply the square root property.

• First solution

`\begin{gathered} v_1+9=2\sqrt[]{5} \\ v_1+9-9=2\sqrt[]{5}-9 \\ v_1=2\sqrt[]{5}-9 \end{gathered}`

• Second solution

`\begin{gathered} v_2+9=-2\sqrt[]{5} \\ v_2+9-9=-2\sqrt[]{5}-9 \\ v_2=-2\sqrt[]{5}-9 \end{gathered}`

Therefore, the solution set in exact form simplest form is:

`\lbrace2\sqrt[]{5}-9,-2\sqrt[]{5}-9\rbrace`