Cube Roots
Radical
A radical is the term under a square root symbol. In the picture above, x would be the radical.
Cube Root
The expression for cube root is a small 3 above the
radical/to the left. This number is
called the index. To calculate the cube
root of a number, we must find the number multiplied by itself, and then
multiplied by itself again, is equaled to the original number.
Problem #1
What is the cube root of 8?
Step 1
We ask ourselves: What number multiplied by itself twice,
equals 8?
Step 2
Guess and check:
Try 2
2 x 2 x 2 = 8
Therefore the cube root of 8 = 2
Answer: 2
Further Explanation
Taking the cube root of a number is the inverse of cubing,
therefore the answer is 2 because 23 = 8.
If Problem #1’s
explanation does not make sense, lets think about what we do when we cube a
number.
To cube a number, we
multiply it 3 times.
For example, when we
cube the number 5:
5 x 5 x 5 = 125
A cube root goes in
the other direction. See Problem #2.
Problem #2
What is the cube root of 125?
Step 1
Use the explanation above.
We know that 5 cubed is 125.
Step 2
So the cube root of 125 is 5
Step 3
5 x 5 x 5 = 125
Answer: 5
Negative Numbers
Problem #3
What is the cube root of -125?
Step 1
As we know, from Problem #2, the cube root of 125 is 5
Step 2
Here, we have -125.
Guess and check. Try -5
Step 3
-5 x -5 x -5 = 125
Answer: -5
Further Explanation
-5 x -5 = 25
25 x -5 = -125
Problem #4
What is the cube root of 0?
Step
1
We ask
ourselves: What number multiplied by itself twice, equals 0?
Step 2
Guess and
check:
Try 0
0 x 0 x 0
= 0
Therefore
the cub root of 0 = 0
Answer: 0
