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5.5 roots and real numbers 5.6 radical expressions - PowerPoint PPT Presentation

5.5 roots and real numbers 5.6 radical expressions. Algebra II w/ trig. The square root of a number and squaring a number are inverses of each other. indicates the nth root

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5.5 roots and real numbers5.6 radical expressions

Algebra II w/ trig

The square root of a number and squaring a number are inverses of each other.

indicates the nth root

n is the index(if there is not a number there, it is an understood 2), # is the radicand, √ is the radical sign

Square Root: if , then a is the square root

of b.

nth root: if then a is an nth root of b.

• Simplify. inverses of each other.

A. B.

C. D.

E. F. G. inverses of each other.

5.6 Radical inverses of each other.Expressions

I. Properties of Square Roots:

A. Product Property of Square Roots

If a andb are real numbers and n>1:

B. Quotient Property of Square Roots

If a andb are real numbers and n>1:

II inverses of each other.. Simplify Completely

A. B.

C. D.

E. inverses of each other. F.

not like expressions

like terms

First, simplify roots, then combine like terms.

A. B.

C. D. inverses of each other.

IV. inverses of each other.Multiplying Radicals by using the FOIL METHOD.

** Multiply the coefficients and the radicands.**

A. B.

• Rationalize – to eliminate radical from a part of a fractional expression

• Generally, you would rationalize a denominator, but you may be asked to rationalize the numerator. So, when not stated always rationalize your denominator.

• To rationalize you must multiply the term(s) by something that causes it to become a perfect root, so the radical can be eliminated.

Example: To eliminate ,you would need to

multiply by . Then their product would be

which can be simplified to 3xy, thus

V. Rationalize the numerator and denominator of each. fractional expression

A . B.

C.D. √

VI. fractional expressionConjugates to rationalize denominator.

The conjugate of a-b is a+b, and vice versa.

A. B.

• Pre-AP – p. 248 # 29-53 odd # 54-61 all fractional expression

p. 254 # 15- 47 odd ( on # 25-29 and 45 rationalize both the denominator and numerator)

p. 255 # 49-55 all

• Algebra II- p. 248 #29 – 53 odd

p. 254 # 15- 47 odd ( on # 25-29 and 45 rationalize both the denominator and numerator)