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Dec. 1 st

Dec. 1 st. HAPPY BIRTHDAY TO: 17 th Paul Marron 18 th Alissa Andi 24 th JJ Mitrokostas 26 th Connor Davis. warm-up: graph both. What is a Radical?. A radical symbol is the symbol √

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Dec. 1 st

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  1. Dec. 1st HAPPY BIRTHDAY TO: 17th Paul Marron 18thAlissaAndi 24th JJ Mitrokostas 26th Connor Davis

  2. warm-up:graph both

  3. What is a Radical? • A radical symbol is the symbol √ • Usually when we see this, we think square root. That’s because there exists a ninja 2 inside the checkmark part of the radical. It’s called an “index”. • The index tells us how many of some number we need to get the number under the symbol. That number is called the “radicand”. √81 = 9 because we need to multiply 2 nines to get 81 2

  4. Symbols • Radical symbol Radical

  5. Principle Square Root Simplify • √4 is an expression, so we only answer the positive version. • √4 = 2 and is called the “principle square root”.

  6. EXAMPLES √9 = 3 Radicand is 9 Index is 2 “square root” We need two of the same number to multiply by each other to get 9…so the answer is 3. √8 = 2 Radicand is 8 Index is 3 “cube root” We need three of the same number to multiply by each other to get 8…so it’s 2. (2 times 2 times 2 is 8) √16 = 2 “fourth root” 3 4

  7. Square Roots 1) Simplify √16 2) Simplify √25 3) Simplify √100

  8. Square Roots • STEPS: • 1. Find the prime factorization (FACTOR TREE). • 2. Take out any groups based off of the index. • 3. If you take out more than one group, multiple the outside numbers. • 4. If you leave in more than one number, multiply the inside numbers.

  9. Simplify: Factor the 12 12 2 6 2 3 Example 4

  10. Prime Factorization 5) Simplify √48 • I like to divide by 2 as many times as I can, then try 3, 5, and so on (to find prime factorization). • Since the index is 2, we are looking for doubles to take out.

  11. Prime Factorization 7) Simplify √54 • I like to divide by 2 as many times as I can, then try 3, 5, and so on (to find prime factorization). • Since the index is 2, we are looking for doubles to take out.

  12. Prime Factorization 8) Simplify √372 • I like to divide by 2 as many times as I can, then try 3, 5, and so on (to find prime factorization). • Since the index is 2, we are looking for doubles to take out.

  13. Another Option 9) Simplify √75 • Another option is to look for perfect squares to take out, such as 4, 9, 16, 25, 100, etc. • Since the index is 2, we are looking for doubles to take out.

  14. Another Option 10) Simplify √200 • Another option is to look for perfect squares to take out, such as 4, 9, 16, 25, 100, etc. • Since the index is 2, we are looking for doubles to take out.

  15. Another Option 11) Simplify √32 • Another option is to look for perfect squares to take out, such as 4, 9, 16, 25, 100, etc. • Since the index is 2, we are looking for doubles to take out.

  16. IMAGINARY NUMBERS…………. • Not all equations have a real-number solution. • Sometimes you could get something like: x2 = -16 • To be able to solve these types of problems the imaginary number was created. √

  17. Complex Numbers Real Numbers Imaginary Numbers RationalIrrational

  18. The Imaginary Unit

  19. Complex Numbers The set of all numbers that can be written in the format: a + bi ; “a” is the real number part “bi’ is the imaginary part

  20. bi 4i 2i + 7i = 9i 8 + i 2i+ 5i= 7i Take the i out first

  21. HOMEWORK • Worksheet

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