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