Here we will explain how to simplify the cube root of 768 (∛768). We start by labeling the parts of ∛768 so it is easy to follow along:
∛768 = 1∛768 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 768 in its simplest form means that you want the radicand to be as small as possible and the coefficient of the radical to be as large as possible.
To simplify the cube root of 768, we first find the greatest perfect cube from the list of factors of 768. The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 64 (4 times 4 times 4 equals 64).
To find the simplified radicand (r) in the cube root of 768, we divide 768 by 64, which gives us 12.
To find the simplified coefficient of the radical (c) in the cube root of 768, we take the cube root of 64, which gives us 4.
That is how you simplify the cube root of 768. Therefore, the cube root of 768 in its simplest radical form is as follows:
∛768 = 4∛12
Simplify Cube Root Calculator
We can do more than simplify the cube root of 768. Enter another cube root below for us to simplify!
Simplify cube root of 769
Here is the next cube root of a number on our list that we have simplified for you.