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College Algebra K /DC Friday, 11 October 2013PowerPoint Presentation

College Algebra K /DC Friday, 11 October 2013

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College Algebra K /DC Friday, 11 October 2013

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- OBJECTIVETSW simplify expressions with radicals.
- ASSIGNMENT DUE TUESDAY, 10/15/13
- Sec. R.6: p. 59 (3-35 all)

- ASSIGNMENT CHANGE FOR TODAY
- Sec. R.7: pp. 70-71 (15-59 odd, 61-76 all)

- QUIZ on Tuesday, 15 October 2013
- Sec. R.6: No calculators, but you may use an exponents chart.

You will do this next week!

R.7

Radical Notations ▪ Simplified Radicals

Notation for a1/n

If a is a real number, n is a positive integer, and a1/n is a real number, then

Notation for am/n

If a is a real number, m is an integer, n is a positive integer, and is a real number, then

A principle square root (principle nth root)isALWAYSpositive!!!

Evaluating___

If n is an even positive integer, then

If n is an odd positive integer, then

Use absolute value only when necessary.

Product Rule

Quotient Rule

Power Rule

If the indices are the same, multiply the radicands (numbers under the radical).

You cannot distribute exponents over a sum!!!!!!

ex:

ex:

- Write each root using exponents and evaluate.

(a)

(b)

(c)

is not a real number.

(d)

- Write each root using exponents and evaluate.

(e)

(f)

- Write in radical form and simplify.

(a)

(b)

(c)

(d)

Test has been moved to Monday, 10/21/13.

- OBJECTIVETSW simplify expressions with radicals.
- ASSIGNMENT DUE
- Sec. R.6: p. 59 (3-35 all) wire basket
- Sec. R.6: p. 60 (47-70 all) black tray

- ASSIGNMENT CHANGE
- Sec. R.7: pp. 70-71 (15-59 odd) due tomorrow
- Sec. R.7: p. 71 (61-76 all) due tomorrow
- Sec. R.7: p. 71 (85-93 all) due test day

- QUIZ: Sec. R.6
- Will be given at the beginning of class
- 20 minutes max to work on it.
- No calculators, but you may use an exponents chart.

- Simplify each expression.

(a)

(b)

(c)

(d)

- Simplify each expression.

(e)

(f)

(g)

- Simplify each expression.

(a)

(b)

(c)

- Simplify each expression.

(d)

(e)

(f)

- Copy the problem, then simplify.

- Copy the problem, then simplify.

- OBJECTIVETSW simplify expressions with radicals.
- ASSIGNMENT CHANGE
- Sec. R.7: pp. 70-71 (15-59 odd) wire basket
- Sec. R.7: p. 71 (62-76 even) due by end of period today
- Sec. R.7: p. 71 (85-93 all) due test day

Test has been moved to Monday, 10/21/13.

R.7

Simplifying, Adding, Subtracting, and Multiplying Radicals

- Simplify each radical.

(a)

(b)

(c)

- NOTE: When adding, subtracting, and multiplying, we will assume that all variables are positive.
- Add or subtract as indicated.

Subtract coefficients

(a)

Same radicand

(b)

Different radicands – simplify first

- Add or subtract as indicated and simplify.

(c)

already simplified

(d)

- Simplify each radical.

(a)

(b)

(c)

- Find the product.

Product of the sum and difference of two terms.

Simplify

- Find the product.

FOIL

- Copy the problem, then simplify.

- Rationalize each denominator.

(a)

“What is the index of the denominator?”

2

(b)

“What will make the denominator a perfect square?”

49

- Simplify the expression.

Simplify radicand.

Quotient rule

Quotient rule

Rationalize denominator.

- Simplify the expression.

Simplify radicand.

Quotient rule

Multiply top and bottom by the conjugate of the denominator.

- Simplify the expression.

Simplify radicand.

Quotient rule

- Simplify the expression.

Simplify radicand.

Quotient rule

- Simplify the expression.

Simplify radicand.

Quotient rule

- Copy the problem, then rationalize the denominator.