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Embrace a last chance to tackle missing assignments and simplify radical expressions with ease. Explore variables, rational exponents, and quadratic applications. Understand solving radical equations and soar in your math journey!
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Last Chance for Missing HW assignments • From now till Lunch you have 2 options • Option 1: • Finish any missing work you might still have from 3rd Quarter, then move on to your homework assignment (Systems and Applications) due Wednesday. • Option 2: • Work and finish your Homework Assignment (Systems and Applications) it is due Wednesday.
Objectives • I can simplify radicals involving variables. • I can simplify higher level radicals. • I can simplify expressions involving rational exponents. • I can solve equations involving radicals and rational exponents.
Opening • We have talked about simplifying radicals for a long time. Today, we are going to take these radicals and push them to the next level. • Using what you know about simplifying radicals, simplify the following radical. You may work with someone next to you as you work.
Simplifying Radical Expressions • Simplifying a radical with variables is the same as if there were only numbers under the radical. • Break down the variable and look for pairs that you can take out.
Try it out! • Rewrite each radical as an exponent or exponent as a radical. 1. 2. 3. 4. 5. 6.
Try it out! • Simplify each radical expression.
Work on HW assignments • From now till Lunch you have 2 options • Option 1: • Work and finish your Homework Assignment (Systems and Applications) it is due Today • Option 2: • Start on new Homework assignment on Rational Exponents(Get it from me)
Rational Exponents • As we mentioned earlier, radicals are fraction exponents. However, we only discussed when the numerator is 1. • We can rewrite all rational exponents as exponents. , where n is an integer and m is any integer.
Simplifying Rational Exponents • Now that we have discussed rewriting radicals with rational exponents, we need to simplify them. • To simplify a rational exponent: • Convert to a radical. • Simplify the radical portion. • Raise the simplified radical to the exponent.
Try it out! • Simplify each expression.
Review • How do solving radical equations relate to solving quadratics? Simplify Write as an exponent.
9 m 12 m The rectangle is 12 m by 9 m. Distance cannot be negative, so we will be using the positive solution
The rectangle is 8ft by 16ft. The rectangle is 15in by 4in.
The rectangle is is 9m by 3m. The garden is 6m by 10m.
45 square feet a) a) b) b) The garden should be 5 ft by 9 ft. The parking space is 9ft wide and 18 ft long.
a) Divide by 2 to get smaller numbers to work with b) Width: 32 in A standard bathtub is 60 inches long. Length:
75 ft Area 50(75) =3750 50 ft a) b) New area needs to be double, 3750(2) =7500 sq ft. or or s feet. This means the owner needs to purchase 12.5 feet of land in every direction to double the size of the lot! The new dimensions would be: 75+12.5+12.5 =100 feet 50+12.5+12.5=75 feet 100(75)=7500
Increasing by 50% works like tax! Multiply by 0.5 then add to the original Area: a) 50% of 43200: b) New Area: 64,800 square ft. feet
Solving Equations • How would you go about solving this problem?
Solving Radical Equations Steps to Solving: Get the radical alone. Get rid of the radical by raising both sides to the same exponent. Solve the equation like normal.
