entire radicals mixed radicals - weebly

3.0 Radicals.notebook

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February 17, 2016

AN2 - Operations on radicals and radical expressions with numerical and variable radicands.

New outcome : Algebra and Number

radical

radicand

index restriction

like radicalssimilar to polynomials

.

Entire Radicals

Mixed Radicals

Converting Entire radicals to Mixed radicals

Perfect Squares

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February 17, 2016

.

Convert the following to mixed radicals.

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February 17, 2016

Convert the following from Mixed to Entire

.

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Write as a mixed radical.

.Page 278­9 #2,3,4, 5, 6

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February 17, 2016

Order the following radicals from least to greatest.

.

Adding and Subtracting Radicals

• you must have like radicals to add and subtract radicals

ex.

ex2.

Page 279#6,8,9, 10

Page 279 #11,13,14,15,16,19, 20

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Multiplying Radicals

-Radicand to radicand-coefficient to coefficient

.

page 289 #1a-d, 2, 3ab, 4abc 5a

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February 17, 2016

Dividing Radicals

* Divide coefficents if possible

* Divide radicands if possible

1. 2.

3.

.

4.

p 290 #6,7

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February 17, 2016

We do not want to have radicals in the denominator

We need to rationalize the denominator to eliminate the radical

.

a)

b)

c)

d)

page 290 #8, 15

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February 17, 2016

More Multiplying...

a)

b)

c)

d)

.

Multiplying by conjugate...

Conjugate: two binomial factors whose product is a difference of squares.(In one binomial there is a + and the other a -)

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February 17, 2016

Rationalize using conjugates...Rationalize the denominator!

.

You try....

b)

a)

page 290 #9, 10, 11, 13

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February 17, 2016

AN3 - Solving Problems that involve radical equations

When solving radical equations, always state restrictions first

Verify all solutions in the original equation to check for extraneous roots

→ Isolate the radical

.

State the restrictions...

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February 17, 2016

Ex 2

Page 300 #,2,3,4

Solve:

An extraneous root is a solution found when solving algebraically that is found not to be a solution when checking the result by substitution.

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.

Solve

.

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Solve

page 300­301 #5,6ab,7abd, 8bc, 10ab

page 301­2

#11, 12, 13, 14, 15, 18, 19

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February 17, 2016

Rational Exponents

First, what is a rational number?

A rational number is a number that can be written as a ratio of two integers.

a where a and b are integers b

Two types of rational numbers

Terminating decimals

Repeating decimals

Rational Exponents

First, what is a rational number?

A rational number is a number that can be written as a ratio of two integers.

a where a and b are integers b

Two types of rational numbers

Terminating decimals

Repeating decimals

.

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February 17, 2016

Rational exponents:

Rational exponents are exponents that are rational numbers, rather self-explanatory, right?

Ex's

There is another way to express a rational exponent, using radicals. The most common radical is the square root.

=

.

In general there are two types of rational exponents:

Simple Roots, where:

When the denominator is 2 we have b ½ = = , the square root, where we normally don't write the 2. When the denominator is 3, we have = which is referred to as the cube root.

Complex roots where:

Convert to radical form:

Convert to exponent form:

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