Homework Solution lesson 8.5 9) X = 12 10) y=− 3 2 11) n = 0 12) M = -3 13) Z = 8 14) T = 5

Homework Lesson 8.7_page 533 #14-19 ALL

Lesson 8.7 Simplifying Radical Expressions

Properties of Radicals For any real number a, 𝑛 𝑎 𝑛 = 𝑎 𝑖𝑓 𝑛 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑒𝑣𝑒𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟, 𝑎𝑛𝑑 𝑛 𝑎 𝑛 =𝑎 𝑖𝑓 𝑛 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑜𝑑𝑑 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 EXAMPLE: (−3) 2 = −3 =3 3 (−3) 3 =−3

Examples 49 𝑥 2 𝑦 5 𝑚 6 Answer: 7 x 𝑦 2 |𝑚 3 | 𝑦

STRUCTURE You can write an expression with rational exponent in radical form 2 4 5 = 5 2 4 = 5 16

Rewrite each expression in radical form (6) 3 2 (7𝑦) 1 4 (2 𝑟 2 ) 4 5

Radicals - definitions The definition of is the number that when multiplied by itself 2 times is x.

Simplifying radicals 1, 4, 9, 16, 25, 36, 49, 64, 81, 100… Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s). The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100… Simplify the radical expression by factoring out as many perfect squares as possible: 48 = 125 = 50 =

Simplifying radicals 1, 8, 27, 64, 125,… 3 48 = 3 125 = 3 100 = The perfect cubes are: 1, 8, 27, 64, 125,… Simplify the radical expression by factoring out as many perfect squares as possible: 3 48 = 3 125 = 3 100 =

Try these - simplify: If a radical has a perfect square factor, then we can pull it out from under the sign. Ex:

Warm-Up # Solve the equation by using the LCD. Check for extraneous solutions. Simplify 𝟐𝒙 𝒙+𝟑 −𝟏= 𝒙 𝒙+𝟑

Homework Solution lesson 8.7 14) 5 2 15) 8 2 16) −3 3 2 17) 64 3 6 18) 4x 2𝑥 19) 3x 2 𝑥

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Lesson 8.7 Adding, Subtracting, and Multiplying Radical Expressions

Combining like-terms 3x+2x – 2 (3+x) + (3 + x) (4 + n) –(-1 -3x)

Adding or Subtracting Radicals To add or subtract square roots you must have like radicands (the number under the radical). Sometimes you must simplify first:

TRY THESE:

Multiplying Radicals You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce.

TRY THESE:

Warm-Up # Simplify 4 250 4+ 7 − −3+2 28 (3+ 2 ) 2

Homework Solution lesson 8.7 45) 6+2 3 46) 7− 7 47) 2− 2 48) −5+5 6 49) −1−10 2 50) −5+15 5 51) −12− 3 52) −1−7 5 53) 1+ 3 54) 23−25 5 55) 12−10 3 56) 34−16 5

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Lesson 8.7 Dividing and Rationalizing Radical Expressions

Dividing Radicals To divide square roots, divide any whole numbers and then divide the radicals one of two ways: 1) divide the numbers under the radical sign and then take the root, OR 2) take the root and then divide. Be sure to simplify. or

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Converting Back and Forth Convert from exponential to radical form: (3) 1/3 (32𝑦) 4/3 Converting from radical to exponential: 4 (3𝑚) 2 8𝑟

Example (64 𝑦 7 ) 1 3 3 𝑦 3

Rationalizing Radicals It is good practice to eliminate radicals from the denominator of an expression. For example: We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways… We need to eliminate Since we will multiply by one where

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