Basic Math and Pre-Algebra For Dummies (19 page)

You can also use ≈ when you estimate the answer to a problem:

In this section, I introduce you to three new operations that you need as you move on with math: exponents, square roots, and absolute value. As with the Big Four operations, these three operations tweak numbers in various ways.

To tell the truth, these three operations have fewer everyday applications than the Big Four. But you'll be seeing a lot more of them as you progress in your study of math. Fortunately, they aren't difficult, so this is a good time to become familiar with them.

Exponents
(also called
powers
) are shorthand for repeated multiplication. For example, 2
³
means to multiply 2 by itself three times. To do that, use the following notation:

In this example, 2 is the
base number
and 3 is the
exponent.
You can read 2
³
as “2 to the third power” or “2 to the power of 3” (or even “2 cubed,” which has to do with the formula for finding the value of a cube — see Chapter
16
for details).

Here's another example:

• 10
  ⁵
  means to multiply 10 by itself five times
  

That works out like this:

This time, 10 is the base number and 5 is the exponent. Read 10
⁵
as “10 to the fifth power” or “10 to the power of 5.”

 When the base number is 10, figuring out any exponent is easy. Just write down a 1 and that many 0s after it:

Exponents with a base number of 10 are important in scientific notation, which I cover in Chapter
14
.

The most common exponent is the number 2. When you take any whole number to the power of 2, the result is a square number. (For more information on square numbers, see Chapter
1
.) For this reason, taking a number to the power of 2 is called
squaring
that number. You can read 3
²
as “three squared,” 4
²
as “four squared,” and so forth. Here are some squared numbers:

 Any number (except 0) raised to the 0 power equals 1. So 1
⁰
, 37
⁰
, and 999,999
⁰
are equivalent, or equal, because they all equal 1.

Earlier in this chapter, in “Knowing Properties of the Big Four Operations,” I show you how addition and subtraction are inverse operations. I also show you how multiplication and division are inverse operations. In a similar way, roots are the inverse operation of exponents.

The most common root is the square root. A
square root
undoes an exponent of 2. For example,

You can read the symbol
 either as “the square root of” or as “radical.” So read
as either “the square root of 9” or “radical 9.”

As you can see, when you take the square root of any square number, the result is the number that you multiplied by itself to get that square number in the first place. For example, to find
, you ask the question, “What number when multiplied by itself equals 100?” The answer here is 10 because