Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) - Mark  Zegarelli


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target="_blank" rel="nofollow" href="#fb3_img_img_6002fc97-4d0f-5204-b1a7-70d956ba5a59.png" alt="math"/> as “10 to the fifth power” or “10 to the power of 5.”

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

1 with two 0s 1 with seven 0s 1 with twenty 0s
math math math

      Exponents with a base number of 10 are important in scientific notation, which I cover in Chapter 17.

      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 math as “three squared,” math as “four squared,” and so forth. Here are some squared numbers:

math

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

      Discovering your roots

      Earlier in this chapter, in the section, “Switching Things Up with Inverse Operations and the Commutative Property,” 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,

math

      You can read the symbol either as “the square root of” or as “radical.” So read math 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 math, you ask the question, “What number when multiplied by itself equals 100?” The answer here is 10 because

math

      You probably won’t use square roots much until you get to algebra, but at that point, they become handy.

      ExampleQ. What is 34?

      A. 81. The expression math tells you to multiply 3 by itself 4 times:

math

      Q. What is math?

      A. 1,000,000. Using the power of ten rule, math is 1 followed by six 0s, so math.

      Q. What is math?

      A. 6. To find math, you want to find a number that, when multiplied by itself, equals 36. You know that math, so math.

      Q. What is math?

      A. 16. To find math, you want to find a number that, when multiplied by itself, equals 256. Try guessing to narrow down the possibilities. Start by guessing 10:

math math

      math, so math is between 10 and 20. Guess 15:

math

      math, so math is between 15 and 20. Guess 16:

math

      This is correct, so math.

      19Your turn Solve these exponents.

      (a) math

      (b) math

      (c) math

      (d) math (Hint: You can make your work


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