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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