An n th root ( ) of b is a solution of the equation. Roots of Real Numbers n is even n is odd If b>0, two real roots. Principal root is positive. If b<0, no real roots. If b>0, or b<0, there is exactly one real root.
Simplify the following roots: Roots of Real Numbers
What is the difference between the following expressions? Roots of Real Numbers
What is the difference between the following expressions? Roots of Real Numbers
Simplify the following: Roots of Real Numbers
Learning Log Summary LT 1 – I can identify the roots of real numbers. The n th root is… If a negative number is in an odd/even root…
Closure Homework (record on Learning Log): LT 1: pg. 262 ~ 1-13 (Odd) pg. 263 ~ Mixed Review 1-5
Consider: and Complete the following property of radicals: Simplifying Radicals
Consider: and Complete the following property of radicals: Simplifying Radicals
The properties we just discovered DO NOT apply to addition and subtraction. CAUTION!!!!
Simplify: Simplifying Radicals
Rationalizing the Denominator means to re-write a fraction with a radical in the denominator so that the only radical is in the numerator. To accomplish this, multiply by some form of 1 so that the denominator can be simplified without a radical. Ex 1) Ex 2) Simplifying Radicals
Learning Log Summary LT 2 – I can simplify expressions involving radicals. To simplify a number without the given root… Rationalizing the denominator means…
Closure Homework (record on Learning Log): LT 2: pg. 267 ~ 1-31 (O), (O)
CONNECT 4 Place any of the items from the answer bank into any space of your Connect 4 board without repeating. You will not use all of the answers! Solve each problem, and if the answer is on the board, place an X in the space. First three people to Connect 4 win!
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Connect 4 Simplify:
Checkpoint #1
Checkpoint #2
Checkpoint #3
Checkpoint #4
Learning Log Summary LT 3 – I can simplify expressions involving the sum of radicals. In order to add or subtract radicals… Roots that can be added or subtracted…
Closure Homework (record on Learning Log): LT 3: pg. 272 ~ 1-25 (O)
Multiplying / Dividing Radical Expressions Simplify the following:
Multiplying / Dividing Radical Expressions Simplify the following:
Multiplying / Dividing Radical Expressions Simplify the following:
Conjugates Notice that the value of is an integer. Expressions of the form and are called conjugates. Multiplying by a conjugate “eliminates” the radicals.
Multiplying / Dividing Radical Expressions Simplify the following:
Multiplying / Dividing Radical Expressions Simplify the following:
Learning Log Summary LT 4 – I can simplify the product and quotients of binomials that contain radicals. When multiplying radicals… If the denominator of a fraction contains a radical expression…
Closure Homework (record on Learning Log): LT 4: pg. 275 ~ 1-29 (O)
Solving Radical Equations Any equation that contains a variable in the radicand is called a radical equation. For example: As a non-example:
Solving Radical Equations REVIEW – What is an extraneous solution ? For Example:
Solving Radical Equations Solve:
Solving Radical Equations Solve:
Learning Log Summary LT 5 – I can solve equations involving radicals. To solve a radical equation… LT 6 – I can identify extraneous solutions to radical equations, using appropriate justifications. An extraneous solution is…
Closure Homework (record on Learning Log): LT 5/6: pg. 280 ~ 1-19 (O) pg. 282 ~ 1-12 (all) QUIZ on MONDAY on LT 1-6