7.2 Calculating with Square Roots
What number do you get if you multiply 3 by itself?

3 · 3 = 9

What number do you get if you multiply 6 by itself?

6 · 6 = 36

Let us reverse the question. What positive number do you multiply by itself to get

a) 4?
b) 16?
c) 25?

3 · 3 can also be written in exponential form.

3 · 3 = 3² = 9

6 · 6 = 6² = 36

You can read more about this in chapter 6.

If we think about the number 49 and imagine which positive numbers are multiplied by themselves which become 49.

x · x = x² = 49

Hopefully you know that this is the number 7 because 7 · 7 = 49.

In mathematics, we have created a sign which shows when we are looking for a positive number multiplied by itself to become the number in question.

The sign is called the square root sign, .

The square root of 49 becomes then 7.

= 7^2/2= 7

= 9^2/2= 9

= 11^2/2 = 11

On your calculator there is often a “square root of button”.

Try for yourself how you use the ”root of button” and try to see what becomes. Remember that the calculator rounds off decimals.

In higher mathematical studies you will be calculating with different types of roots.  There are even “root laws”.

Now you hopefully know that = 3, that = 4,and that = 5.

What do you think that and   becomes? Guess first and then check with your calculator.

Hint: You are looking for and know that = 3 and = 4, lies between these numbers.

Summary: