Square Root Graphing Calculator Online

What is Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For any non-negative real number x, the square root is written as √x. For example, √9 = 3 because 3 × 3 = 9.

Square roots can be calculated for both perfect squares (like 16, 25, 36) and non-perfect squares (like 2, 3, 5). The calculator handles both cases accurately.

Square Root Properties

• √(a × b) = √a × √b
• √(a/b) = √a/√b
• √(a²) = |a|

How to Use This Calculator

Using the square root graphing calculator is simple:

1. Enter the number you want to find the square root of in the input field.
2. Select whether you want to calculate the square root or graph the function.
3. Click the "Calculate" button to get the result.
4. View the result and graph (if applicable) in the result section.

The calculator provides both the numerical result and a visual representation of the square root function when graphing is selected.

Graphing Square Roots

Graphing square root functions helps visualize how the square root changes as the input value changes. The basic square root function is y = √x.

The graph of y = √x is a curve that starts at the origin (0,0) and increases gradually as x increases. It never goes below the x-axis.

Transformations of Square Root Functions

You can transform the basic square root function by applying transformations:

• Vertical stretch: y = a√x
• Horizontal stretch: y = √(x/h)
• Reflection: y = -√x
• Vertical shift: y = √x + k
• Horizontal shift: y = √(x - h)

Worked Examples

Example 1: Simple Square Root

Find √16.

Solution: √16 = 4 because 4 × 4 = 16.

Example 2: Non-Perfect Square

Find √2.

Solution: √2 ≈ 1.41421356237 because 1.41421356237 × 1.41421356237 ≈ 2.

Example 3: Graphing y = √x

Graph the function y = √x for x values from 0 to 10.

Solution: The graph starts at (0,0) and increases gradually, passing through points like (1,1), (4,2), and (9,3).