Solve each equation and check the solution. 08 September 2015 Warm-Up.

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1 Solve each equation and check the solution. 08 September 2015 Warm-Up

2 Squares and Square Roots Definitions: Square: Multiplying a number, variable or expression by itself. Square Root: A number, variable or expression that is a factor when multiplied by itself. Examples Find the square root of the following:

3 Squares and Square Roots There is a HUGE difference between using a calculator to find the value of the square root and finding the EXACT value of a square root. Perfect Square: Any number that is created by multiplying a rational number by itself.

4 Sometimes a PERFECT SQUARE is not so obvious. What is the Square Root of Squares and Square Roots Since is a repeating decimal, you will need to recognize that is a rational number equivalent. So, in fact is a perfect square.

5 Prime Numbers: Any number whose only factors are 1 and itself. Prime Factorization: Reducing any number to the product of Prime Numbers. Squares and Square Roots 5 is a Prime Number because you can only multiply 1 and 5 to get the product 5. Prime Numbers: 2, 3, 5, 7, 11, 13, 17 ….. NOTE: There are infinitely many Prime Numbers. 12 is not a Prime Number because it has more factors than just 12 and 1.

6 Squares and Square Roots Look at this product that equals 12 in particular Since the numbers 2 and 3 are Prime Numbers, this product represent the Prime Factorization of 12. You will need to use the Prime Factorization of numbers to find the EXACT value a number that is NOT a Perfect Square. If you use a calculator to find the APPROXIMATE value of 12, you will get the following. The best you are likely to do is get a number rounded to 2 or 3 decimal places. The EXACT VALUE will have a Square Root term in the answer.

7 Squares and Square Roots Handy Rules for Prime Factorization 1)If the number is even then 2 is a factor. 2)If the sum of the digits in the number add up to a multiple of 3 then 3 is a factor. 3)If the number ends with a 5 or a 0 then 5 is a factor. EXAMPLE:540 ends in a 0 so 5 is a factor, it is even so 2 is a factor and the digits add to 9 so 3 is a factor.

8 Squares and Square Roots Now, to find the EXACT value of the Square Root of 540 use the Prime Factorization. Any Questions?

9 Squares and Square Roots There are two important rules you need to remember. Product Property of Square Roots: Quotient Property of Square Roots:

10 Squares and Square Roots Find the EXACT value and the APPROXIMATE value of the following.

11 September 08, 2015 Homework Copy and find the exact value and the approximate value of the following expressions.