Laws of Exponents (Warm-Up) (1) (2) (3)

Homework Go over homework answers/problems

Radicals

Radicals Radicand Index COEFFICIENT

Simplifying Radicals "Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power.  For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3. So does anybody know what we call numbers like: 4, 9, 16, 25, 36, 49…..  

So what are the “Perfect Squares”?

Steps to Simplifying Radicals (that are not perfect squares) Simplifying Radicals that are square roots Create a factor tree Identify any factor that is a perfect square That perfect square “pair” will come outside the radical and be multiplied by the existing coefficient All other factors will remain inside the radical as part of the radicand

Simplifying Radicals

200 𝑣 7 𝑟 10 28𝑥 4

What about if the Index Changes?

Adding and Subtracting Radicals Must have the same radicand and index Only add and subtract the number outside the radical

Adding and Subtracting Radicals

Adding and Subtracting Independent Practice

More Practice Adding and Subtracting

Multiplication of Radicals Multiplying Radicals only need same index to multiply multiply numbers on the outside of the radical separately than numbers on the inside of the radical must simplify the final answer as far as possible

Multiplication of Radicals

Multiplication of Radicals

Multiplication of Radicals Multiplying Radicals only need same index to multiply multiply numbers on the outside of the radical separately than numbers on the inside of the radical must simplify the final answer as far as possible

Warm-Up Problems & Homework 𝑥 7 𝑥 15 (2) (−3 𝑧 2 ) 2 (3) 28𝑥 −2 7𝑦 −3 (4) (−2 𝑟 −4 𝑠 2 ) −3 (5) Simplify 525 (6) Simplify -7 28 𝑥 5 𝑦 6

Multiplication of Radicals

What Happens When…. We Square a Radical Term? We Square a Binomial with a Radical? We are asked to Multiply a Binomial with a Radical by another Binomial with a Radical?

Multiplication of Radicals ( 4 𝑥 2 𝑦 3 + −2𝑥 ) 2

More Practice Multiplying Radicals

Division of Radicals Dividing radicals Cannot have a fraction under a radical Cannot have a radical in the denominator (called rationalizing the denominator) Multiply top and bottom by the bottom radical Simplify your answer

Division of Radicals

Division of Radicals Practice

More Practice With Division of Radicals

Worksheet Division of Radicals

REVIEW PROBLEMS 1)

REVIEW PROBLEMS 6) −6 5− 6

SOLVING RADICAL EQUATIONS

Solving Simple Radical Equations So, if we try to solve….. 𝑦 = 5 …… then what is y? And if 2𝑥 = 8 …. then what is x = ?

Challenge Problems Solve for x 3𝑥 = 9 Solve for y 4 𝑦 −1 = -8 (2) (1) (4) (3) Solve for x 3𝑥 = 9 Solve for y 4 𝑦 −1 = -8

YOUR TURN Solve: 𝑥 = 2 Solve: 9𝑦 = 12 𝑚 4 = 3

Solving Radical Equations 𝑥 −2 - 1 = 5 (4) 𝑣+15 = 5 + 𝑣 so what happens if the equation has more than one radical? 3𝑧 −5 = 4 (5) 𝑥+12 − 𝑥 = 3 𝑥 −15 = 𝑥 - 3 (6) 9𝑛−9 - 2𝑛−1 = 3

Worksheet on ALEKS REVIEW and Solving Radical Equations

Applications of Radical Equations (1) (2)

Rational Exponents

Rational Exponents 𝑛 𝑎 𝑚 = 𝑎 𝑚 𝑛 and

RATIONAL EXPONENTS

RATIONAL EXPONENTS

RATIONAL EXPONENTS

RATIONAL EXPONENTS