Simplifying Square Root Expressions[In Class Version][Algebra 1 Honors].notebook August 26, Homework Assignment. Example 5 Example 6.

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1 Homework Assignment The following examples have to be copied for next class Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Example 9 Example 10 Example 11 Example 12 The examples must be copied and ready for me to check once you come to class. Aug 26 6:02 PM 1

2 Simplifying Square Roots The, ( square root of b ) means to find a number that when multiplied with itself the product is equal to b. In this lesson we will use the symbol denote the positive square root of a number. Jul 19 6:13 PM 2

3 First 20 Perfect Square Integers Jul 19 6:06 PM 3

4 Example 1 Evaluate : SOLUTION 3 Jul 19 6:23 PM 4

5 Example 2 Evaluate : SOLUTION No Real Solution Whenever there is a negative number under the square it is not possible to get a real number. Jul 19 6:29 PM 5

6 Example 3 Evaluate : SOLUTION 3 If the negative sign is NOT inside the square root just take the square root of 9, and keep the negative sign. Jul 19 6:37 PM 6

7 Example 4 Evaluate : SOLUTION 3 Jul 19 6:37 PM 7

8 Example 5 Evaluate : SOLUTION Jul 19 6:40 PM 8

9 Example 6 Evaluate : SOLUTION 5 Jul 19 6:41 PM 9

10 Simplifying & Evaluating square roots that are not perfect squares. 1. Rewrite the number under the radical as the product of two factors. Very important one of the factors has to be a PERFECT SQUARE (never use 1 as your perfect square factor). *[If there is more than 1 perfect square factor use the largest one.] 2. Give each factor it s own square root. 3. Simplify the square root, and rewrite the expression. Jul 19 6:45 PM 10

11 Example 7 Evaluate : SOLUTION The number 12 is not a PERFECT SQUARE. There are 3 ways that the number 12 can be written as product of two factors : or or For this 1st example try to simplify using each option to show why it is necessary to use a factor that is a perfect square(excluding the number 1). Jul 19 6:51 PM 11

12 Let's start off with the factors of : Replace the 12 under the square root with : Give each factor its own square root. Simplify the square roots, if possible. The square root of 1 can be simplified to 1. Now multiply the square root 12 and 1, the product is the square root of 12. Even though 1 is a perfect square it should not be used as a factor because you will end up with the original problem. Jul 19 6:51 PM 12

13 Let's use the factors of : Replace the 12 under the square root with : Give each factor its own square root. Simplify the square roots, if possible. The square root of 6 or the square root of 2 cannot be simplified without the use of a calculator. Using these factors we cannot go any further. Jul 19 7:15 PM 13

14 Let's use the factors of : Replace the 12 under the square root with : Give each factor its own square root. Simplify the square roots, if possible. Jul 19 7:15 PM 14

15 Example 8 Evaluate : SOLUTION The number 150 is not a PERFECT SQUARE. The remainder is not zero so 144 is not a perfect square factor so now try 121. The remainder is not zero so 121 is not a perfect square factor so now try 100. Jul 19 7:48 PM 15

16 The remainder is not zero so 100 is not a perfect square factor so now try 81. The remainder is not zero so 81 is not a perfect square factor so now try 64. The remainder is not zero so 64 is not a perfect square factor so now try 49. The remainder is not zero so 49 is not a perfect square factor so now try 36. Jul 19 7:48 PM 16

17 The remainder is not zero so 36 is not a perfect square factor so now try 25. The remainder is zero so 25 is a perfect square factor of 150. Jul 20 11:25 AM 17

18 Example 9 Evaluate : SOLUTION The number 243 is not a PERFECT SQUARE. The remainder is not zero so 225 is not a perfect square factor so now try 196. The remainder is not zero so 196 is not a perfect square factor so now try 169. Jul 20 10:38 AM 18

19 The remainder is not zero so 169 is not a perfect square factor so now try 144. The remainder is not zero so 144 is not a perfect square factor so now try 121. The remainder is not zero so 121 is not a perfect square factor so now try 100. The remainder is not zero so 100 is not a perfect square factor so now try 81. Jul 20 10:54 AM 19

20 The remainder is zero so 81 is a perfect square factor of 243. Jul 20 11:06 AM 20

21 Example 10 Evaluate : SOLUTION The number 30 is not a PERFECT SQUARE. The largest perfect square integer than is less than 30 is 25. Start with 25 and continue this process until a perfect square factor is found or we get to the number one. The remainder is not zero so 25 is not a perfect square factor so now try 16. Jul 20 11:15 AM 21

22 The remainder is not zero so 16 is not a perfect square factor so now try 9. The remainder is not zero so 9 is not a perfect square factor so now try 4. The remainder is not zero so 4 is not a perfect square factor and we should never use the number one. This is an example to show that not all numbers can be simplified further. Jul 20 11:24 AM 22

23 Simplifying variable expressions under a radical. If the exponent is EVEN divide the exponent by 2. This quotient will be the new exponent and expression will be written without a radical. EXAMPLES Jul 31 6:38 PM 23

24 Simplifying variable expressions under a radical. If the exponent is ODD rewrite an equivalent expression that is the product of two powers. The first power will be raised to the original exponent minus 1 and the second power will have an exponent of 1. EXAMPLES Aug 1 10:04 AM 24

25 Example 11 Simplify : SOLUTION Aug 26 5:52 PM 25

26 Example 12 Simplify : SOLUTION Aug 1 10:48 AM 26