College algebra k dc friday 11 october 2013
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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 dc friday 11 october 2013

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!


Radical expressions

Radical Expressions

R.7

Radical Notations ▪ Simplified Radicals


Radical definitions

Radical Definitions

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 n th root

Principle Square Root / Principle nth Root

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


Radical definitions1

Radical Definitions

Evaluating___

If n is an even positive integer, then

If n is an odd positive integer, then

Use absolute value only when necessary.


Radical definitions2

Radical Definitions

Product Rule

Quotient Rule

Power Rule

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


Caution

CAUTION !!!!!

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

ex:

ex:


Evaluating roots

Evaluating Roots

  • Write each root using exponents and evaluate.

(a)

(b)

(c)

is not a real number.

(d)


Evaluating roots1

Evaluating Roots

  • Write each root using exponents and evaluate.

(e)

(f)


Converting from rational exponents to radicals

Converting From Rational Exponents to Radicals

  • Write in radical form and simplify.

(a)

(b)

(c)

(d)


College algebra k dc tuesday 15 october 2013

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

Using Absolute Value to Simplify Roots

  • Simplify each expression.

(a)

(b)

(c)

(d)


Using absolute value to simplify roots1

Using Absolute Value to Simplify Roots

  • Simplify each expression.

(e)

(f)

(g)


Using the rules for radicals to simplify radical expressions

Using the Rules for Radicals to Simplify Radical Expressions

  • Simplify each expression.

(a)

(b)

(c)


Using the rules for radicals to simplify radical expressions1

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

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 dc wednesday 16 october 2013

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.


Radical expressions1

Radical Expressions

R.7

Simplifying, Adding, Subtracting, and Multiplying Radicals


Simplifying radicals

Simplifying Radicals

  • Simplify each radical.

(a)

(b)

(c)


Adding and subtracting like radicals

Adding and Subtracting Like Radicals

  • 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


Adding and subtracting like radicals1

Adding and Subtracting Like Radicals

  • Add or subtract as indicated and simplify.

(c)

already simplified

(d)


Simplifying radicals by writing them with rational exponents

Simplifying Radicals by Writing Them With Rational Exponents

  • Simplify each radical.

(a)

(b)

(c)


Multiplying radical expressions

Multiplying Radical Expressions

  • Find the product.

Product of the sum and difference of two terms.


Multiplying radical expressions1

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

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

  • Copy the problem, then simplify.


Rationalizing denominators

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

Simplifying Radical Expressions with Fractions

  • Simplify the expression.

Simplify radicand.

Quotient rule

Quotient rule

Rationalize denominator.


Simplifying radical expressions with fractions1

Simplifying Radical Expressions with Fractions

  • Simplify the expression.

Simplify radicand.

Quotient rule

Multiply top and bottom by the conjugate of the denominator.


Simplifying radical expressions with fractions2

Simplifying Radical Expressions with Fractions

  • Simplify the expression.

Simplify radicand.

Quotient rule


Simplifying radical expressions with fractions3

Simplifying Radical Expressions with Fractions

  • Simplify the expression.

Simplify radicand.

Quotient rule


Simplifying radical expressions with fractions4

Simplifying Radical Expressions with Fractions

  • Simplify the expression.

Simplify radicand.

Quotient rule


Assignment sec r 7 p 71 85 93 all due monday 21 october 2013

Assignment: Sec. R.7: p. 71 (85-93 all)Due Monday, 21 October 2013

  • Copy the problem, then rationalize the denominator.


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