Pg. 122 from Student Journal Complete 1-13 Bellwork Pg. 122 from Student Journal Complete 1-13 Algebra II

Bellwork Problems Algebra II

Bellwork Problems cont.. Algebra II

BW cont… Algebra II

nth Roots and Rational Exponents 5.1 nth Roots and Rational Exponents Algebra II

“the nth root of x to the mth” Vocabulary Pg. 125 SJ exponent index exponent base radicand “x to the nth power” “the nth root of x to the mth” Algebra II

State the index and the radicand for each. SJ Pg. 125 *an index of 2 is understood if one is not written 1. √10 2. 3√81 3. 7√92 4. 4√p index: 2 radicand: 10 index: 3 radicand: 81 index: 7 radicand: 92 index: 4 radicand: p Algebra II

Rational Exponent Rules SJ Pg. 126 Algebra II

Write each using rational exponents. SJ Pg. 126 (Notes) 1. √x = 2. 3√y2 = 3. 8√52 = 4. 4√95 = x ½ y 2/3 5 2/8 = 5 1/4 9 5/4 Algebra II

Write each using radicals. SJ pg. 126 (Notes) 1. 3 2/9 = 2. 4 3/10 = 3. 6 2/3 = 4. x 9/4 = 9√32 10√43 3√62 4√x9 Algebra II

SJ Pg. 127: 12-15 Matching Algebra II

Simplifying nth Radicals Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144… Cube Roots 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000… Fourth Roots 1, 16, 81, 256, 625, 1296… Fifth Roots 1, 32, 243, 1024, 3125… Algebra II

Find each without a calculator 1. 3√-125 = 2. 4√16 = 3. 5√-32 = 4. 3√27 = 5. 93/2 = 6. 32 -2/5 = 7. 165/2 = 8. 64-2/3 = -5 2√93 = 33 = 27 1 = 1 = 1 5√322 22 4 2 -2 2√165 = 45 3 1 = 1 = 1 3√642 42 16 Algebra II

Student Journal Pg. 124 Evaluate each without a calculator. Algebra II

Student Journal Pg. 126 Evaluate each without a calculator. Algebra II

Student Journal Pg. 123 Use a calculator to find each value Algebra II

SJ Pg. 125 Algebra II

Solve each using nth roots: real answers only. 1. 2x4 = 162 x4 = 81 4√x4 = 4√81 x = ±3 2. (x – 2)3 = 10 3√(x – 2)3 = 3√10 x – 2 = 3√10 x = 2 + 3√10 Only put a ± when the index is even! Algebra II

Solve each using nth roots: real answers only. 3. 2(y - 1)5 = -64 (y – 1)5 = -32 5√(y – 1)5 = 5√-32 y – 1 = -2 y = 1 – 2 y = -1 4. 2(x + 1)2 = 72 (x + 1)2 = 36 2√(x + 1)2 = 2√36 x + 1 = ± 6 x = -1 ± 6 x = -1+6 x = -1-6 x = 5 x = -7 Only put a ± when the index is even! Algebra II

SJ Pg. 127: 16-19 Algebra II

SJ Pg. 127 Algebra II

Simplifying nth Radicals Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144… Cube Roots 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000… Fourth Roots 1, 16, 81, 256, 625, 1296… Fifth Roots 1, 32, 243, 1024, 3125… Algebra II

Simplify each. 1. 3√54 2. 4√64 Cube Roots: 1,8,27,64,125,216,343 1. 3√54 Cube Roots: 1,8,27,64,125,216,343 3√54 = 3√27∙2 = 3√27∙3√2 = 33√2 2. 4√64 Fourth Roots 1,16,81,256 4√64 = 4√16∙4√4 = 2 4√4 Algebra II

Simplify each. 3. 3√48 4. 4√162 Cube Roots: 1,8,27,64,125,216,343 3. 3√48 Cube Roots: 1,8,27,64,125,216,343 3√48 = 3√8∙6 = 3√8∙3√6 = 23√6 4. 4√162 Fourth Roots 1,16,81,256 4√162 = 4√81∙4√2 = 3 4√2 Algebra II

Manipulative Activity √ Algebra II

Simplify each. 5. 3√250y7 6. 3√125∙2∙y7 5y2 3√2y Cube Roots: 1,8,27,64,125,216,343 3√125∙2∙y7 5y2 3√2y 6. Algebra II

Simplify each. 7. 3√81z5 8. 4√162x9 3√81z5 = 3√27∙3∙z5 = 3z 3√3z2 Cube Roots: 1,8,27,64,125,216,343 3√81z5 = 3√27∙3∙z5 = 3z 3√3z2 8. 4√162x9 Fourth Roots 1,16,81,256 4√162x9 = 4√81∙2∙x9 = 3x2 4√2x Algebra II

Simplify each. 9. 3√56x3z5 10. 4√48x12y15 3√8·7x3z5 = 2xz 3√7z2 Cube Roots: 1,8,27,64,125,216,343 3√8·7x3z5 = 2xz 3√7z2 10. 4√48x12y15 Fourth Roots 1,16,81,256 4√48x12y15= 4√16∙3x12y15 = 2x3y3 4√3y3 Algebra II

Application Problems 1. The equation to estimate wind chill temperature C, for an air temperature of 5° F and a wind speed of s miles per hour is C = 69.2(0.94s) – 50. What would the windchill temperature be if the wind speed is 20 mph. Algebra II

Application Problems 2. The shot used in men's shot put has a volume of about 905 cubic centimeters. Find the radius of the shot. Round to the nearest hundredth. (Hint: Use the Formula V= 4/3πr3) Algebra II

Application Problems Algebra II

Application Problems Algebra II

Closure: Exit Pass 1. 2. 3. 4. 5. 1, 5 Algebra II