Exponents & Square Roots DO NOW Solve the following problems (no calculator): 1). - 8 + - 16 = 2). -4 + 7 = 3). 15 + -111 = 4). 19 + 11 = 5). -17 + - 19 - 6). -90 + 17 =

What are we doing Today OBJECTIVE: WE WILL be able to write and solve exponential and square root equations ESSENTIAL UNDERSTANDING: 1). Multiplication is repeated addition; exponents are repeated multiplication. 2). Exponents and square roots are opposite sides of the same coin AP

Review: Multiplication vs Exponents Multiplication is repeated addition: 4 x 2 = 4 + 4 = 8 4 x 5 = 4 + 4 + 4 + 4 + 4 = 20 Exponents are repeated multiplication: 42 = 4 x 4= 16 45 = 4 x 4 x 4 x 4 x 4 = 1024 AP

Exponent Vocabulary Remember Base and Power! - A base to the second power is sometimes called “squared”. 42 is four “squared”. - A base to the third power is sometimes called “cubed”. 53 is five “cubed”. AP

Writing Exponents Let’s do these together: Write the following exponents 1). 6 x 6 x 6 x 6 = 2). 8 x 8 x 8 = 3). 5 x 5 x 5 x 5 x 5 = 4). 3 x 3 = AP

Solve the Following Exponents Let’s do these together: Solve the following exponents 1). 23 = 2). -42 = 3). 54 = 4). 33 = AP

Independently: Write the following exponents 1). 2 x 2 x 2 x 2 = 2). 9 x 9 x 9 x 9 x 9 = 3). 4 x 4 x 4 x 4 x 4 x 4 = 4). 6 x 6 = AP

Independently: Solve the following exponents 1). 22 = 2). -23 = 3). 33 = 4). 43 = AP

What is a Square Root? A square root is the opposite of an exponential square. 32 = 9 and √9 = 3 22 = 4 and √4 = 2 On a calculator, input the number and the √ key and you will receive the square number AP

Let’s Practice Find the Square Roots of the Following Numbers: 1). 1 2). 2 3). 3 4). 4 5). 8 6). 9 7). 16 8). 100

Perfect Squares Perfect Squares are numbers whose square roots are whole numbers: Number Square Number Square 1 1 6 36 2 4 7 49 3 9 8 64 4 16 9 81 5 25 10 100

Independent Practice For the following numbers, find the square and the square root: 1). 1 2). 4 3). 9 4). 8 5). 116 6). 100 7). 225 6). 400 9). 912