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College Algebra K /DC Friday, 11 October 2013. OBJECTIVE TSW 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

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College Algebra K /DC Friday, 11 October 2013

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### College Algebra K/DCFriday, 11 October 2013

• 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

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

### Principle Square Root / Principle nth Root

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).

### CAUTION !!!!!

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

ex:

ex:

### Evaluating Roots

• Write each root using exponents and evaluate.

(a)

(b)

(c)

is not a real number.

(d)

### Evaluating Roots

• Write each root using exponents and evaluate.

(e)

(f)

### Converting From Rational Exponents to Radicals

• Write in radical form and simplify.

(a)

(b)

(c)

(d)

### College Algebra K/DCTuesday, 15 October 2013

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.

### Using Absolute Value to Simplify Roots

• Simplify each expression.

(a)

(b)

(c)

(d)

### Using Absolute Value to Simplify Roots

• Simplify each expression.

(e)

(f)

(g)

### Using the Rules for Radicals to Simplify Radical Expressions

• Simplify each expression.

(a)

(b)

(c)

### Using the Rules for Radicals to Simplify Radical Expressions

• Simplify each expression.

(d)

(e)

(f)

### Assignment: Sec. R.7: pp. 70-71 (15-59 odd)Due today, Wednesday, 16 October 2013

• Copy the problem, then simplify.

• Copy the problem, then simplify.

### College Algebra K/DCWednesday, 16 October 2013

• 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

• 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)

(b)

Different radicands – simplify first

• Add or subtract as indicated and simplify.

(c)

(d)

### Simplifying Radicals by Writing Them With Rational Exponents

• Simplify each radical.

(a)

(b)

(c)

### Multiplying Radical Expressions

• Find the product.

Product of the sum and difference of two terms.

### Multiplying Radical Expressions

Simplify

• Find the product.

FOIL

### Assignment: Sec. R.7: p. 71 (62-76 even)Due today, Wednesday, 16 October 2013 black tray

• Copy the problem, then simplify.

### Rationalizing Denominators

• Rationalize each denominator.

(a)

“What is the index of the denominator?”

2

(b)

“What will make the denominator a perfect square?”

49

### Simplifying Radical Expressions with Fractions

• Simplify the expression.

Quotient rule

Quotient rule

Rationalize denominator.

### Simplifying Radical Expressions with Fractions

• Simplify the expression.

Quotient rule

Multiply top and bottom by the conjugate of the denominator.

### Simplifying Radical Expressions with Fractions

• Simplify the expression.

Quotient rule

### Simplifying Radical Expressions with Fractions

• Simplify the expression.

Quotient rule

### Simplifying Radical Expressions with Fractions

• Simplify the expression.