Graphing square roots on a simple number line might seem like the hardest thing in the world. Yet it is actually quite simple. There are two methods of doing this. The first method would be with a calculator. The second would involve several steps. The first method should take no longer than 15 seconds. The second method would take a minute or so for smaller numbers, and the time will increase exponentially as the number gets larger.
Things You'll Need
 Calculator

Skip to Step 2 if you are not using a calculator. Press the square root sign on the calculator. Input the number and press "Enter." Jot down the number on a sheet of paper. Skip to Step 3.

Take a rough estimate of the square root. Make sure that it is a whole number. Using your pencil and paper, square that number. Increase and decrease until you find two consecutive numbers, one bigger and smaller than the number in the original square root.

Draw a line. If you did not use the calculator, plot five or so points around the two consecutive numbers you found. If you used a calculator, plot five or so of the whole numbers before and after the number.

Determine which of the two consecutive numbers your square root is closer to. If it is closer to the lesser one, plot the point a little closer to that number. If the number is closer to the greater one, plot the point a little closer to that number. For example, √19 would be between √16, or 4, and √25, or 5. But 19 is closer to 16 than 25, so you would plot √19 proportionally closer to 4 than 5.
Then mirror your number on the negative side of the number line and plot it out. For example, if your number is the square root of 16, which is 4, you should plot both 4 and 4 on the number line. This is because 4 squared is the same as 4 squared.
Tips & Warnings
 Knowing how to do this without a calculator will help when situations come along when you don't have a calculator.
References
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