5.5 roots and real numbers 5.6 radical expressions

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.

5.6 Radical 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. 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)

5.5 roots and real numbers 5.6 radical expressions