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5.5 roots and real numbers 5.6 radical expressions

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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.
A. B.

C. D.

E. F.G.

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. Simplify Completely

A.B.

C. D.

E.F.

III. Adding/Subtracting radicals: add only like radicals(same index and same radicand)

not like expressions

like terms

First, simplify roots, then combine like terms.

A.B.

C.D.

IV. 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

eliminating the radical.

V. Rationalize the numerator and denominator of each.

A.B.

C.D. √

VI. Conjugates 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
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)