Cube Roots To understand cube roots first you

Cube Roots

To understand cube roots, first you must understand cubes. . . How to Cube A Number ? To cube a number, just use it in a multiplication 3 times. . . Example: What is 3 Cubed? 3 Cubed = = 3 × 3 = 27 Note: we write down "3 Cubed" as 33 (the little "3" means the number appears three times in multiplying)

Some More Cubes 4 cubed = 43 = 4× 4× 4 = 64 5 cubed = 53 = 5× 5× 5 = 125 6 cubed = 63 = 6× 6× 6 = 216 7 cubed = 73 = 7× 7× 7 = 343 8 cubed = 83 = 8× 8× 8 = 512

Cube Root A cube root goes the other direction: 3 cubed is 27, so the cube root of 27 is 3 27 3 The cube root of a number is. . . the special value that when cubed gives the original number. The cube root of 27 is. . . 3, because when 3 is cubed you get 27. Note: When you see "root" think "I know the tree, but what is the root that produced it? " In this case the tree is "27", and the cube root is "3".

Here are some more cubes and cube roots: Example: What is the Cube root of 125? Well, we just happen to know that 125 = 5 × 5 (if you use 5 three times in a multiplication you will get 125). . . so the answer is 5

The Cube Root Symbol This is the special symbol that means "cube root", it is the "radical" symbol (used for square roots) with a little three to mean cube root. You can use it like this: (you would say "the cube root of 27 equals 3")

You Can Also Cube Negative Numbers Have a look at this: If you cube 5 you get 125: 5 × 5 = 125 If you cube -5 you get -125: -5 × -5 = -125 So the cube root of -125 is -5

Perfect Cubes The Perfect Cubes are the cubes of the whole numbers: 1 2 3 Perfect 1 8 27 Cubes: 4 5 6 7 8 9 10 11 12 13 14 etc 64 125 216 343 512 729 1000 1331 1728 2197 2744 …

Cube roots of numbers other than perfect cubes Example: what is the cube root of 30? 3 × 3 = 27 and 4 × 4 = 64, so we can guess the answer is between 3 and 4. Let's try 3. 5: 3. 5 × 3. 5 = 42. 875 Let's try 3. 2: 3. 2 × 3. 2 = 32. 768 Let's try 3. 1: 3. 1 × 3. 1 = 29. 791 We are getting closer, but very slowly. . . at this point, I get out my calculator and it says: 3. 1072325059538588668776624275224. . . but the digits just go on and on, without any pattern. So even the calculator's answer is only an approximation !