Do Now 4/12/19 Take out HW from last night. Copy HW in your planner. Text p. 485, #8-36 evens, #46-54 evens Copy HW in your planner. Text p. 485, #56-60 evens, #76-90 evens Go Formative and simplify the following expressions.

Homework Text p. 485, #8-36 evens

Homework Text p. 485, #8-36 evens

Homework Text p. 485, #46-54 evens

Learning Goal Learning Target SWBAT simplify, graph, and define characteristics of radical functions and solve quadratic equations   Learning Target SWBAT use properties of radicals to simplify expressions, simplify expressions by rationalizing the denominator, and perform operations with radicals. 

Section 9.1 “Properties of Radicals” A radical expression is in simplest form if the following conditions are true: The rules also apply for simplifying cube roots and nth roots. No perfect square factors other than 1 are in the radicand. -No fractions are in the radicand. No radicals appear in the denominator of a fraction.

Product Property of Radicals The square (or cube) root of a product equals the product of the square ( or cube) roots of the factors.

Quotient Property of Radicals The square root of a quotient equals the quotient of the square roots of the numerator and denominator.

Rationalizing the Denominator Whenever there is a radical (that is not a perfect square) in the denominator, the radical must be eliminated by rationalizing the denominator. Need to rationalize the denominator Multiply by 1 Product property of radicals Simplify

Real World Connections The orbital period of a planet is the time it takes the planet to travel around the Sun. You can find the orbital period P (in Earth years) using the formula , where d is the average distance (in astronomical units AU) of a planet from the Sun. a). Simplify the formula. b). What is Jupiter’s orbital period.

Real World Connections c). One step further. Search the Internet for the AUs for another planet. Calculate the orbital period.

Adding and Subtract Radicals Part 2 Adding and Subtract Radicals You can add and subtract radicals that have the same radicands. Think of as combining ‘like terms’ Look for common radicands Simplify

Try It Out…

Multiplying Radical Expressions You can multiply radical expressions the same way you multiplied monomials and binomials using the distributive property and FOIL. simplify & combine like terms

Try It Out… simplify & combine like terms

Conjugates Need to use a conjugate to Multiply by 1 rationalize the denominator Multiply by 1 Product property of radicals simplify & combine like terms Simplify

Try It Out… Need to use a conjugate to Need to use a conjugate to rationalize the denominator Need to use a conjugate to rationalize the denominator Multiply by 1 Multiply by 1 Simplify Simplify

Clock Partners With your 6:00 partner, complete text p. 485, #13, 17, 23, 27, 31, 33, 47, 51, 55, 57, 83, & 87