In this lesson, you will learn how to solve a square root equation using tables and graphs as well as how these two methods are connected. You will begin by solving using tables first. It's important to understand domain, so that you can determine the appropriate values for your table.

Let's begin with an example.

Example 1: y = √(x + 3)

How do you know what x-values are acceptable for this problem's table?

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The acceptable x-values for the table are elements of the domain of the function.

How do you find the domain?

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The value under the radical sign should be positive because you cannot take the square root of a negative number. Set the expression under the radical sign equal to or greater than zero and solve. These values are your domain.

Find the domain for this problem.

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Set x + 3 ≥ 0, so x ≥ -3. The domain is x ≥ -3.

Complete the table below.

You can do so by substituting the values in the X column into the equation above to get the Y values. For example, substituting -3 into the equation gives you y = √(-3 + 3) = √0 = 0. Click in the empty spaces in the Y column to reveal the remaining Y values.

Use the table to answer the following questions.

1. Can the x-values be less than -3? Why?

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   No, the x values less than -3 would result in a negative value under the square root, which would be an imaginary number. Values less than -3 are not in the domain.

2. As the x-values increase, what happens to the y-values?

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   As the x-values increase, the y-values also increase.

Example 2: The equation y = 8√x gives y, the speed in feet per second of an object in free fall after falling x feet.

1. Which column represents the number of feet the object has fallen? (X or Y)

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   The values in the X column represent the number of feet the object has fallen.

2. Which column represents speed a free falling object? (X or Y)

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   The values in the Y column represent the speed of a falling object.
3. Use the table below to find the speed of an object in free fall after it has fallen 16 feet.
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4. Use the same table to find the height of a free falling object when it has a speed of 16 ft/s.

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   4 ft

Using a table is one way to solve square root functions. In the next section, you will solve square root equations by using graphs.