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 =
3^{2} = 9
6 · 6 =
6^{2} = 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 =
x^{2} = 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. 
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. 

Summary: 
