Algebra 2 - EPSD
Algebra 2 Name________________________
Notes 7-1 Date____________Period______
7-1: Roots and Radical Expressions
Def: The nth root of an equation: For any real numbers [pic] and [pic], and any positive integer [pic], if [pic] then [pic] is the nth root of [pic].
|Type of Number |Number of Real nth Roots When n Is Even |Number Of Real nth Roots When n is Odd |
|Positive | | |
|0 | | |
|Negative | | |
Radical Expressions Vocab
• [pic]
• The principal root is the positive root of a number that has a positive and negative root.
Property: nth root of [pic]
• For any negative real number [pic], [pic] when [pic] is even.
Ex: Simplify each radical expression
[pic] [pic] [pic]
[pic] [pic] [pic]
HW: ______________________________________________
Algebra 2 Name________________________
Notes 7-2 Date____________Period______
7-2: Multiplying and Dividing Radical Expressions
Multiplying Radical Expressions
• If [pic] and [pic] are real numbers, then [pic].
Ex: Multiply and simplify answer if necessary.
• [pic]
• [pic]
• [pic]
• [pic]
• [pic]
• Simplify [pic]. Assume all variables are positive.
Dividing Radical Expressions
• If [pic] and [pic] are real numbers and [pic], then [pic].
Ex: Divide. Assume all variables are positive.
[pic] [pic] [pic]
Rationalizing the denominator
• To be in simplest form, a radical expression should have all perfect roots taken out of the radicand, and it should not have a radical in the denominator.
Ex: Rationalize the denominator of each expression. Assume all variables are positive.
[pic] [pic] [pic]
[pic] [pic] [pic]
HW: _________________________________________________
Algebra 2 Name________________________
Notes 7-3 Date____________Period______
7-3: Binomial Radical Expressions
Like Radicals are radicals that have the same index and the same radicand. If radical terms are “like”, we can add or subtract them.
Ex: Add or subtract if possible. It may be necessary to simplify the radicals first to see if you have like terms.:
[pic] [pic] [pic]
[pic] [pic]
Multiplying and Dividing Binomial Radical Expressions
Ex: [pic] [pic]
[pic] [pic]
Rationalizing Binomial Denominators
• Multiply by a fraction of [pic]. Simplify.
[pic] [pic]
HW: _________________________________________________________
Algebra 2 Name________________________
Notes 7-4 Date____________Period______
7-4: Rational Exponents
Another way to write a radical expression is with a rational (fraction) exponent. See the examples below:
[pic]
Try these. Simplify each expression:
[pic] [pic] [pic]
[pic] [pic]
What to do when the numerator of a rational exponent is other than 1:
• If the [pic] root of [pic] is a real number and [pic] is an integer, then
[pic] and [pic]. If [pic] is a negative, [pic].
Ex: Convert from radical to rational exponent form, or vice versa.
[pic] [pic] [pic] [pic]
Ex: Simplify:
[pic] [pic] [pic]
[pic] [pic] [pic]
[pic] [pic]
HW: _________________________________________________________
Algebra 2 Name________________________
Notes 7-5 Date____________Period______
7-5: Solving Radical Equations
• Isolate the radical expression/rational exponent on one side of the equation.
• Raise both sides of the equation to the same power. (If trying to undo a square root, square both sides. If trying to undo a cube root, cube both sides. If solving for an x raised to the [pic] power, raise both sides to the [pic], etc.)
• Check for extraneous roots! Plug your answer(s) back into the original equation to make sure they work!
Ex: Solve
[pic] [pic]
[pic] [pic]
[pic] [pic]
HW: ______________________________________________________________
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