7 47 5 Simplify AddSub MultDiv Radicals Simplify

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals Simplify, Add/Sub, Mult/Div SWBAT § Simplify radical expressions. SWBAT Simplify and evaluate Holt. Mc. Dougal Algebra 2 Algebra Holt 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals In plain words… The "nth Root" used n times in multiplication gives the original value "nth“ 2 nd, 3 rd, 4 th, 5 th, . . . nth. . . Instead of talking about the "4 th", "16 th", etc, if we want to talk generally we say the "nth“ The nth Root: The "2 nd" root is the _________ The "3 rd" root is the __________ SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals Academic Vocab: The nth Root Notation Radical sign index Radicand Reading Math When a radical sign shows no index, it represents a square root. SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals The nth power and its inverse We already learned in the last section that: and are inverses of each other. The inverse of raising a number to the nth power is to find the nth root SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

The Principal Root Some numbers have more than one real nth root. The non-negative root is called the principal root. This indicates the square root of 16 This indicates the opposite of the square root of 16 This indicates both square roots of 16 This indicates the cube root of -125

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals A. sixth roots of 64 A positive number has two real sixth roots. Because 2 6 = 64 and (– 2)6 = 64, the roots are 2 and – 2. B. cube roots of – 216 A negative number has one real cube root. Because (– 6) 3 = – 216, the root is – 6. C. fourth roots of – 1024 A negative number has no real fourth roots. SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals Simplify: SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

The nth root of an even power When we square a negative (or put it to an even power) we get a positive, therefore when taking an even root, we must make sure our answer is negative! Simplify:

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals Think-Pair-Share SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.

7 -4&7. 5 Simplify, Add/Sub, Mult/Div Radicals HOMEWORK • Page 405 – #14 -36 Even SWBAT Simplify and evaluate Holt Mc. Dougal Algebra 2 radical expressions and expressions.