Cubed Roots
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by Lonnie Myers
| 7 Questions
Note from the author:
Cube roots
1
1
Find the surface area and the volume of the cube
The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six.

Finding the volume of a cube is a snap - generally, all that's needed is to multiply the cube's length × width × height. Since a cube's sides are all equal in length, another way of thinking of a cube's volume is s3, where s is the length of one of the cube's sides.
The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six.

2
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A different cube has a side of length 5.  Write two expressions that would represent how to find the volume of the cube.  One expression should use exponents.
3
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Now reverse the process.  If you know the volume, how long is the side?  Given the volumes of different cubes below.
a.) 8 cubic units
b.) 125 cubic meters
c.) 1000 cubic feet
d.) 40 cubic inches
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In problem 3 did you find the solution by guessing and checking, or did you find a special key on your calculator that helped?  Watch the video below to learn about the special cube root key on the graphing calculator
5
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Is the number rational or irrational. Explain how you know
6
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Just like with perfect squares and square roots, cube roots of perfect cubes are positive integers.  Some of them are listed below.
Without a calculator, you can approximate the cube root to be between consecutive integers, as you did with square roots.

Approximate the following cube root between consecutive integers.

7
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How do you find the length of the side of a cube if you know its volume?  What is this operation called? Create examples that demonstrate what you know about cube roots and how to find them.