Goal: Calculate a square root.
What is a square root?
The square root of a number n is the number that when multiplied by itself will equal n.
It's not too hard to understand. The square root of 49 is 7, because 7 x 7 = 49. That's all.
The bad news is that most square roots are harder than that because you end up with a decimal. The good news is that most calculators do have the square root symbol, and that you are allowed to use one for this whole section.
The square root of 49 is called a perfect square, because the answer is a whole number. Other perfect squares include 4 (2 x 2), 9 (3 x 3), and 16 (4 x 4).
The symbol for a square root is called a radical. It looks like this:
When you see this symbol with a number, it is a math problem. For example, this:
is read, "the square root of 8."
What do I need this for?
Suppose you are asked to decide the dimensions of a workspace that will be 120 square feet. One way to do it is to find the square root of 120, which is about 10.95. Then you can have a perfectly square office space with the right floor area. Of course, you could also have other dimensions, like 12 x 10. But I like things to be perfectly square, and since I'm in charge that's just the way it's gonna be.
Example 1:
Find the square root of 36.
Solution
The answer is 6, because 6 x 6 is 36. 36 is a perfect square.
Example 2:
Find the square root of 12.25.
Solution
You need a calculator. Most calculators have the square root symbol as one of their keys. On some, you may need to press a "shift" button first. You press the symbol first, and then the number, and then the equal sign.
The correct answer is 3.5, because 3.5 x 3.5 = 12.25.
Example 3:
A square has an area of 15 square feet. What is the length of its sides?
Solution
The square root of 15 is 3.87. Each side is 3.87 feet long.
You try it:
You want to create 75 square feet of office space in the shape of a square. What should be the dimensions of the square?