d ec. 1 st happy birthday to: 17 th paul marron 18 th alissa andi 24 th jj mitrokostas 26 th connor...
TRANSCRIPT
DEC. 1ST
HAPPY BIRTHDAY TO:17th Paul Marron 18th Alissa Andi24th JJ Mitrokostas 26th Connor Davis
WARM-UP:GRAPH BOTH
3 | 1| 2y x
2 3y x
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
SYMBOLS
Radical symbol
#Index Radicand
Radical
PRINCIPLE SQUARE ROOT
√4 is an expression, so we only answer the positive version.
√4 = 2 and is called the “principle square root”. Simplify
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
SQUARE ROOTS
1) Simplify √16
2) Simplify √25
3) Simplify √100
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.
EXAMPLE 4
Simplify: Factor the 12
12 2 6
2 3
12
2 2 3
2 2 3
2 3
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.
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.
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.
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.
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.
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.
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.
√
1i
Complex Numbers
Real Numbers Imaginary Numbers
Rational Irrational
THE IMAGINARY UNIT
11 2 iwherei
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
1) 16 22) b
3) 4 49 4) 64 1
5) 4 25
4i bi
2i + 7i = 9i 8 + i
2i + 5i = 7i Take the i out first
HOMEWORK
Worksheet