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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.

= 72/2= 7

= 92/2= 9

= 112/2 = 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.

Foto: Fredrik Enander

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.


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