RATIONAL EXPONENTS Algebra One

Explore in your Notebook… Evaluate the following: b) c) – d) e) f) g) h) What is an irrational number? What is a rational number? How can we predict/determine when a square root is irrational or rational? List the first 15 perfect squares.

Perfect Squares It’s important to know your perfect squares – they can be useful for estimating values for irrational square roots. Estimate the following square roots without a calculator:

SQUARING and SQUARE-ROOTING are INVERSE OPERATIONS. IMPORTANT FACT SQUARING and SQUARE-ROOTING are INVERSE OPERATIONS.

Can we take roots other than “square roots”? Yes we can take any kind of root – for example: The cube root of 8 is noted as The fifth root of 32 is noted as

SQUARE ROOTS & Nth ROOTS Yes we can take any kind of root – for example: The square root of any number: The nth root of any number: *the “index” of the radical tells you what root you are taking, if you don’t see an “n” then it is square root.

What does this have to do with EXPONENTS? Consider… roots and powers are inverse operations square root squaring Cube root cubing Fourth root fourth power Nth root nth power

If you could turn a “root” into a power, what would it look like? Remember – inverse operations “cancel” out. so is the same as so is the same as

RATIONAL EXPONENTS The nth root of a positive number can be written as a power with base “a” and exponent “1/n”

RATIONAL EXPONENTS This makes nth roots very easy to evaluate on our calculator, just remember to put parentheses around the full exponent.

Get comfortable going back & forth between radical & exponential notation for nth roots. Write the following using rational exponent notation: a) b) Write the following using radical notation. c) d) 61/9 e) Seventh root(s) of 13

What about Rational Exponents that do NOT have a numerator of ONE? What does this mean? 163/4 consider reversing the power of a power property 163/4 = 1631/4 = (163)1/4 So what does that numerator represent?

RATIONAL EXPONENTS The nth of a positive number can be written as a power with base “a” and exponent “1/n”

This makes it quite easy to evaluate on your calculator if you remember how to rewrite them!

Cool Down – THINK ABOUT IT… What is the meaning of a negative rational exponent? 8-4/3

Homework Worksheet – Radicals & Rational Exponents