Powers and Radicals without Calculators (6.5)

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Presentation transcript:

Powers and Radicals without Calculators (6.5) Using a factor tree when your calculator goes on the fritz

A little review Let’s look again at yesterday’s exponential problems we simplified: (6x5)(3x-2) (5x-4)(2x-3) (-2x2)3(3x-1y2)4 (x-1y-4z)/(x-2yz-3) (3x-1/2)(4x2/3) (3758x89)(3758x-89) (u3.7p4.8)/(u-2.9p1.8)

A POD warm-up Rewrite each of the following using a radical sign: 81/3 2431/5 Can you figure out what they equal without using a calculator?

Let’s look more closely 81/3 What is the factor tree for 8? How could we use that to find the final answer?

Let’s look again more closely 2431/5 What is the factor tree for 243? How can we use it to find a final answer?

Now try this Use a factor tree to find 2561/4. Use it to find 641/3.

Let’s mix it up a bit What is 2431/5? What would 2433/5 equal then?

You design one Write a power expression with a fraction exponent that equals 2. We’ve seen that 81/3 will do this. Any others? How about one that equals 4?

Signs -2431/5 equals -3 2561/4 equals 4 641/3 equals 4 So, we can take: the even root of a positive number. the odd root of a positive number. the odd root of a negative number. But we cannot take: the even root of a negative number (remember finding the square root of a negative number?)