10.2.2 Repeating Square Roots
Activity: Repeating Square Roots
Work out . Now, click on to find . Keep repeating this so that you are finding and , and so on. What do you notice happening?
Each calculation needs just . Watch the windows at the top of the calculator to see what is happening.
If you keep taking square roots of the answer, the number gets closer and closer to 1. Try starting with a different number, like 37. Does the same happen? What about a number between 0 and 1, such as 0.5?
Activity: Square Roots of Negative Numbers
What do you think the square root of –16 is? It can’t be –4, because , not –16. Use the calculator to find the answer.
Enter the square root, then –16 using the ± button.
You should get an answer like this:
Notice that the 4i in the black screen is colored green. This is to show you that you have a different type of number. In this context, “i” is shorthand for . This is known as an imaginary number. You will learn more about imaginary numbers if you continue studying mathematics. However, for the moment, it is sufficient to know that the square root of a negative number can’t be found among the ordinary numbers that you work with every day. If you have a hand calculator, you could try finding the square root of a negative number on it; you may find that it displays an error message.
- To find a square root on the calculator, use the key, remembering to close the parentheses after you have entered the number.