1、.Are You Hip to be Square?We are going to take a look at the “roots” of a number by finding the square root of rational numbers.Rational Numbers? What is a rational number?Rational Numbers are numbers that can be written as fractions of integers. They can be written as a quotient of two integers. Th

2、e decimal representation of a rational number will either stop or repeat and go on forever.Recall: Squaring a number, a number that is a number times Itself.1. 42 exponent = tells you how many times to use the base as a factorBase = this is the factor that you are multiplying 2. 42 = 4×4 3. 42

3、= 4×4 = 16When you multiply a number by itself, you are squaring that number. 3 x 3 is 9; therefore, 3 squared equals nine. 8 x 8 is 64, so 8 squared is 64. Another way to write these problems is with the exponent 2 (that little number up in the air). For example 82 is read as "eight squar

4、ed". Note: The inverse (opposite) of squaring a number would be finding the “square root” of a number. Just like adding and subtracting are inverse operations of one another, finding the square root of a number is the inverse of squaring a number. The square root of a number x looks like this T

5、he square root of a number ,x, is the number that gives ,x, when multiplied by itself.Example: because We can also look at numbers that are called Perfect Squares. This simply means we are squaring the whole numbers. 1x1 = 12 = 12x2 = 22 = 43x3 = 32 = 94x4 = 42 = 165x5 = 52 = 25A perfectly squared n

6、umber is simply a number that can be made of 2 identical factors that when squared equal that number. 36 is another perfect square because it has a factor 6 that when multiplied by itself will equal 36. 6 x 6 = 36. Since both factors are identical you can also write it as 62. List 10 more perfect sq

7、uare numbers after 36:But, we know that all things are not perfect so how would we find the square root of a number that does not have a set of factors that are identical: What is the square root of 10 or ?We use the square roots of perfect squares to estimate the square root of non-perfect square n

8、umbers. We can get very exact with these non-perfect numbers if we choose to use a calculator, but we want to start with simply estimating to find an approximation of the square root of non-perfect numbers.Finding Square root of Non-Perfect Numbers:1. Start with an estimation, look for 2 perfect squ

9、are numbers that the number you are looking for the square root of falls between., the perfect square numbers that would be before this number and after are . The square root of 9 would be 3 and the square root of 16 is 4. This means that the square root of 10 would be a number somewhere between 3 and 4. What would this number look like? Since 3 and 4 are consecutive whole numbers what is left are the numbers in between or parts of a whole number. This would leave us with a fraction or decimal. 10 is much closer to 9 than it is 16 so the square root of 10 will be closer to 3 than 4.What