Converting Between Radicals & Rational Exponents Unit 4, Lesson 3 Converting Between Radicals & Rational Exponents

11/30 Do Now *Please start a new Do Now sheet! Solve for h if V= 1 3 bh Write a function (y=mx+b) to represent the sequence: -12, -11.75, -11.5, -11.25…? The equation y= 461.19x + 3492 represents the value of a work of art from 1964 to 2005. What does the number 461.19 represent? In 1983, the average price of a home was $50,000. By 2008, the average price of a home is $200,000. What is the annual rate of change?

What did we learn last week? Multiplying exponents, dividing exponents, and negative exponents Let’s review: y7 * y-3 g4p5 p2 14x-5 (h7d3)(h-2d6)

Square Number Also called a “perfect square” A number that is the square of a whole number Can be represented by arranging objects in a square.

Square Numbers What do you notice about the table?

Perfect Squares A Perfect Square: is “perfect” because its square root is a whole number. Can you name any other perfect squares? Example: is a perfect square because = 49

Non-Perfect Squares A Non-Perfect Square: is a number whose square root is NOT a whole number. Example: is NOT a perfect square because = 40 6.3245…

How are radicals & exponents related? What is a radical? Includes three separate parts: the index, the radicand, and the actual radical Identify each part of the following expression: How are radicals & exponents related? Inverses! We can say that radicals “undo” exponents, and exponents “undo” radicals.

How to rearrange radical & exponent equations Remember, 2 × 4=8 can be rearranged into 8 ÷ 4=2 In the same way, we can say 3 8 =2 rearranges into 2 3 =8. Examples: Rewrite 2 16 =4 into an equation with only integers and exponents. Rewrite 4 3 =64 into an equation that includes a radical. How did the index, radicand, and base change?

Good news! We can rewrite numbers with fractions as exponents using a radical! Definition of a1/n If n is a positive integer greater than 1 and 𝑛 𝑎 is a real number, then 𝑎 1/𝑛 = 𝑛 𝑎 . What this means…….. Let’s look at an example: 8 1 3 = You try: 4 1 2 = 27 1 3 = 3 8 81 1 4 = 32 1 5 =

as long as 𝑛 𝑎 is a real number. MORE good news! We’re not just limited to exponents that are a 1/n fraction! Definition of am/n If m and n are positive integers greater than 1, and 𝑚 𝑛 is reduced, then am/n = 𝑛 𝑎 𝑚 𝑜𝑟 𝑛 𝑎 𝑚 as long as 𝑛 𝑎 is a real number. For example, 82/3 = 3 8 2 . You try: −27 2 3 = −32 3 5 = 1 16 3/2 =

EOC Practice Simplify 3 8𝑥2𝑦3𝑧4

EOC Practice Which expression is equivalent ( 𝑥 1/3 ) −3 ? 𝑥 1 𝑥 1 𝑥9 1 𝑥27

Exit Ticket Make sure to put your name on your paper! If 9 1 2 × 9 1 2 simplifies to 9, then what do you think 𝑧 1 4 × 𝑧 1 4 × 𝑧 1 4 × 𝑧 1 4 simplifies to?