Solve equations involving cubes and cube roots
key notes :
Taking the cube root (∛) is the inverse of cubing. For example, ∛27=3 since 27=33.
A perfect cube is the result when an integer is multiplied by itself, and then multiplied by itself again. For example, 27 is a perfect cube because 3.3.3=27. The cube root of a perfect cube is always an integer.
Learn with an example
Look at this equation:
a3 =125
What is a, the cube root of 125?
a=___
You want to find the cube root of 125, so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals 125.
The number 5 cubed equals 125.
53 =5.5.5=125
In other words, the equation a3 =125 is true when a=5.
So the cube root of 125 is 5.
Look at this equation:
t3 =8
What is t, the cube root of 8?
t=____
You want to find the cube root of 8, so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals 8.
The number 2 cubed equals 8.
23 = 2.2.2 =8
In other words, the equation t3 =8 is true when t=2.
So the cube root of 8 is 2.
Look at this equation:
s3 = 27
What is s, the cube root of 27?
s=
You want to find the cube root of 27, so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals 27.
The number 3 cubed equals 27.
33=3.3.3=27
In other words, the equation 33=27 is true when s=3.
So the cube root of 27 is 3.
Let’s practice!
