10.2.2 Repeating Square Roots

Activity Symbol Activity: Repeating Square Roots

Work out Square root of two. Now, click on The buttons shown are the square root button followed by the equals button. to find Square root of Square root of two. Keep repeating this so that you are finding Square root of Square root of Square root of two and Square root of Square root of Square root of Square root of two, and so on. What do you notice happening?

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Comment

Each calculation needs just The buttons shown are the square root button followed by the equals button.. Watch the windows at the top of the calculator to see what is happening.

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Answer

Square root of two equals 1.414 full stop full stop full stop 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 Symbol Activity: Square Roots of Negative Numbers

What do you think the square root of 16 is? It can’t be 4, because four minus multiplication four minus equals 16, not 16. Use the calculator to find the answer.

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Enter the square root, then 16 using the ± button.

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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 Square root of super minus times one. 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 recap:

  • To find a square root on the calculator, use the The button shown is the square root key. key, remembering to close the parentheses after you have entered the number.

10.2.1 Calculator Exploration: Square Roots

10.2.3 Calculator Exploration: Cube Roots and More