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:

1. (6x5)(3x-2)2. (5x-4)(2x-3)3. (-2x2)3(3x-1y2)4

4. (x-1y-4z)/(x-2yz-3) 5. (3x-1/2)(4x2/3)

6. (3758x89)(3758x-89)7. (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?

What would (2431/5)3 equal?

What would 243-1/5 equal?

What would -2431/5 equal?

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?)