A.9 Day 2 nth Roots Rational Exponents Radical Equations...
16
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010 1 September 22, 2010 Jan 211:37 PM A.9 DAY 2 n th Roots Rational Exponents Radical Equations Objectives: Work with n th Roots Simplify Radicals
Transcript of A.9 Day 2 nth Roots Rational Exponents Radical Equations...
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
1
September 22, 2010
Jan 211:37 PM
A.9 DAY 2n th RootsRational ExponentsRadical Equations
Objectives:Work with n th Roots
Simplify Radicals
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
2
September 22, 2010
Nov 37:32 AM
List the squares and cubes of the numbers 1‐10.Follow this format.
12 = 22 = 32 = 42 = 52 = 62 = 72 = 82 = 92 = 102 =
Warm‐up
13 = 23 = 33 = 43 = 53 = 63 = 73 = 83 = 93 = 103 =
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
3
September 22, 2010
Jan 212:32 PM
Roots
A radical sign is used to indicate a root.
The index gives the degree of the root.
The number under the radical sign is the radicand.
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
4
September 22, 2010
Jan 212:32 PM
Every positive real number has two square roots, one positive and one negative.
For example: The two square roots of 49 are 7 and ‐7.
The positive square root is also known as the
principal square rootand is denoted with a radical sign: √49 = 7.
Roots
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
5
September 22, 2010
Jan 231:58 PM
Simplify each expression.
1. 2. 3.
√an = |a| if n is even and n ≥ 2.n
√25 √81 √-100
Even Roots
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
6
September 22, 2010
Jan 212:32 PM
Every real number has exactly one cube root.
For example: √8 = 2 AND √‐8 = ‐23 3
Roots
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
7
September 22, 2010
Jan 231:58 PM
Simplify each expression.
1. 2. 3.
√an = a if n is odd and n ≥ 3.n
∛-8
Odd Roots
∛27 ∛ 16125
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
8
September 22, 2010
Jan 232:10 PM
Simplifying Radicals
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
9
September 22, 2010
Jan 191:24 PM
Example: Simplify each expression. Assume that all variables are positive.
a. √72x3 b. ∛80n5
c. √50x4 d. ∛18x4
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
10
September 22, 2010
Jan 191:23 PM
Example: Multiply. Simplify if possible.
a. √2 √8 b. ∛5 ∛25 c. √-2 √8
d. √3 √12 e. ∛3 ∛9 f. ∜4 ∜4
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
11
September 22, 2010
Jan 191:25 PM
Example: Multiply and simplify. Assume that all variables are positive.
∛54x2y3 ∛5x3y4
∛270x5y7
∛27x3y6 10x2y
3xy2∛10x2y
3√7x3 2√21x3y2b.a.
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
12
September 22, 2010
Jan 610:52 AM
Example: Divide and simplify. Assume that all varaibles are positive.
a. ∛32 32 ∛4 4
b. ∛162x5 162x5 ∛3x2 3x2
=
√= 3 =∛8 = 2
√3 = ∛54x3 = ∛27x3(2) = 3x∛2
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
13
September 22, 2010
Jan 241:11 PM
Like radicals are radical expressions that have the same index and the same radicand. We can add and subtract like radicals.
Add or subtract if possible.
a. 5∛x - 3∛x b. 4√2 + 5√3 c. 2√7 + 3√7
d. 7∜5 - 2∛5 e. 4√xy + 5√xy
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
14
September 22, 2010
Jan 241:18 PM
√50 + 3√32 - 5√18
6√18 + 4√8 - 3√72a.
b.
Simplifying Before Adding or Subtracting
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
15
September 22, 2010
Jan 241:53 PM
You can multiply radical expressions that are in the form of binomials by using FOIL.
Simplify each expression by multiplying.
a. (3 + 2√5)(2 + 4√5) b. (√2 - √3)2
A.9 Day 2 nth Roots_Rational Exponents_Radical Equations 2010
16
September 22, 2010
Jan 232:10 PM
Homework:page 1037(7 16,19 22,25 31)
