Simplify: BELLWORK

CHECK HOMEWORK

RADICALS AND RATIONAL EXPONENTS Evaluate square roots Use the product rule to simplify square roots Use the quotient rule to simplify square roots Add and subtract square roots Rationalize denominators Evaluate and perform operations with higher roots Understand and use rational expressions

MIND MAP Radicals/Square Roots

SQUARE ROOTS Radical sign Radicand

EVALUATE THE SQUARE ROOTS

MORE INFORMATION ABOUT SQUARE ROOTS

a) Find b) Find c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

If a and b represent nonnegative real numbers, then THE PRODUCT RULE FOR SQUARE ROOTS The square root of a product is the product of the square roots The product of two square roots is the square roots of the product of the radicands

a) Use a calculator to approximate to two decimal places b) Use a calculator to approximate to two decimal places c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

A SIMPLIFIED SQUARE ROOT

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BELLWORK

HOMEWORK:

a) Find b) Find c) Based on your answers to parts (a) and (b), what can you conclude? TRY THIS:

THE QUOTIENT RULE FOR SQUARE ROOTS The square root of a quotient is the quotient of the square roots The quotient of two square roots is the square root of the quotient of the radicands

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YOU DO

ADDING AND SUBTRACTING RADICALS To be able to add or subtract radicals, they must have the same radicand and the same index.

COMBINING SQUARE ROOTS

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WE DO

YOU DO

Sometimes we have to simplify radicals before we can add or subtract them. At first the terms might not look like they can be combined, so we have to simplify first. COMBINING RADICALS THAT REQUIRE SIMPLIFICATION FIRST

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Add or subtract whenever possible EXIT TICKET

TB pg. 46 (#23-43 odd) HOMEWORK:

Multiply: (F.O.I.L.) BELLWORK:

When we say that we are going to rationalize the denominator, we are rewriting the rational expression so that we no longer have a radical in the denominator. Multiply the numerator and denominator by the smallest number that produces the square root of a perfect square in the denominator. RATIONALIZING THE DENOMINATOR Multiplication by 1 does not change the value of the rational expression. But what does it mean to multiply by 1, and how can this help us rationalize a denominator?

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CONJUGATES

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TB pg. 46 (#45-53 odd) CLASS WORK:

Finish Class Work: If necessary Quiz next Friday on sections P-2 & P-3 Simplifying exponential and radical expressions HOMEWORK

BELLWORK

CLASSWORK ANSWERS

OTHER ROOTS Radical sign Radicand Index

ROOTS OF REAL NUMBERS

If n is odd, If n is even, NTH ROOTS OF PERFECT NTH POWERS

Evaluate CUBE ROOTS

Evaluate 4 TH ROOTS

5 TH ROOTS

Evaluate: I DO

Evaluate WE DO:

Evaluate YOU DO:

PRODUCT AND QUOTIENT RULES FOR OTHER ROOTS and

I DO

Simplify BELLWORK

HOMEWORK ANSWERS

Adding and subtracting nth roots is very similar to adding and subtracting square roots. Sometimes we will need to simplify first. Remember: They must have the same index and radicand!!!! COMBINING NTH ROOTS

Add or subtract whenever possible I DO

Add or subtract whenever possible WE DO

Add or subtract whenever possible YOU DO

GROUP ACTIVITY

What rules did your group come up with? How did you get to this rule, what thinking led you there? Do you think this rule will work for every radical? REFLECTION

Evaluate without using a calculator BELLWORK

HOMEWORK ANSWERS

DEFINITIONS

Now that we know how to write a radical as a rational exponent, what properties do you think apply?

Simplify using properties of exponents I DO:

Simplify using properties of exponents WE DO:

Simplify using properties of exponents YOU DO:

Simplify by reducing the index of the radical. Sometimes, problems are easier to simplify if we can reduce the index first SIMPLIFYING

For exponents(p-2): Product Rule Quotient Rule Zero Exponent Rule Negative Exponent Rule Power Rule Power of a product rule Power of a quotient rule Simplifying exponential expressions For Radicals (P-3): Evaluating square and higher roots Product rule for square and higher roots Quotient rule for square and higher roots Adding and subtracting square roots Rationalizing denominators Rational Exponents YOU NEED TO KNOW:

TB pg (#24-31) (#41-71) These are just practice problems, they are to help guide you to what you need to study most. I would recommend doing a few from each section to gauge your understanding QUIZ REVIEW

TB pg (# odd) Study for tomorrow’s quiz HOMEWORK: