Warm Up:. 5.1 Notes: nth Roots and Rational Exponents.

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Presentation transcript:

Warm Up:

5.1 Notes: nth Roots and Rational Exponents

What is a radical?  A radical is a symbol for finding the root of a number. This could be a square root, cube root, 4 th root, 5 th root, etc.  Even roots:  = 2 real roots, one positive & one negative  = 0  = no real roots, an “i” would need to be used.

 Odd roots:  = one real root that is positive, because “a” is positive  = 0  = one real root that is negative, because “a” is negative  EX: Find each root –  1) 2) 3) 4)

Evaluating Expressions with Rational Exponents (No Calculator)  Evaluate …..How? Well, we split the fraction up.  Change this to …the numerator goes on the outside, the denominator stays on the inside. Evaluate the root (the fraction) first, then take the exponent of that answer.

 Evaluate:  A) B) C)

Rational Exponents  Question: Can we type in to the calculator? What about ?  How can we find the answers without having to do factor trees?  ANSWER: Rational exponents  Rational exponents: exponent(power) root  So, = =

Now what?  Now, we can type these into our calculators:  216 ^ (1 ÷ 3) =  ( ) ^ (2 ÷ 7) =  You try:

What do we do to solve equations with exponents?  We use SADMEP to solve them, just that we will need to remember to use the reciprocal power when doing opposite operations!  If your original exponent was EVEN you will have TWO answers, a positive and a negative one!  Round all answers to the hundredths place.

Examples:  A) x 4 = 60B) x 1/2 = 12C) 2(x + 2) 3 = 54  D) (x – 6) 2/5 = 37E) x = 2153  F) 2x -1/2 + 6 = 16

HW:  P. 241 – 242 #11 – 31 odd, 35 – 43 odd