Question

5 more than the square root of the difference of a number and 2 is 13. What is the number?

Answer 1

Step-by-step explanation:

Let the number = x

`\begin{gathered} \text{The difference of the number and 2}=x-2 \\ The\text{ square root }=√(x-2) \\ 5\text{ more than the square root}=\sqrt[]{x-2}+5 \end{gathered}`

The result is 13, therefore, we have the equation:

`\sqrt[]{x-2}+5=13`

We solve the equation for x:

Subtract 5 from both sides.

`\begin{gathered} \sqrt[]{x-2}+5-5=13-5 \\ \sqrt[]{x-2}=8 \end{gathered}`

Next, square both sides: