Whats the answer to 3√216
The Correct Answer and Explanation is :
The cube root of 216 is ( \sqrt[3]{216} = 6 ).
Explanation:
A cube root is the inverse operation of cubing a number. To find the cube root of a number, we need to find a number that, when multiplied by itself three times (cubed), gives the original number.
In this case, we are trying to find the cube root of 216, which means we are looking for a number that satisfies this equation:
[
x^3 = 216
]
Let’s check by cubing different numbers:
- ( 1^3 = 1 )
- ( 2^3 = 8 )
- ( 3^3 = 27 )
- ( 4^3 = 64 )
- ( 5^3 = 125 )
- ( 6^3 = 216 )
We see that ( 6^3 = 216 ), so the cube root of 216 is 6.
More about cube roots:
Cube roots are typically denoted with the radical symbol ( \sqrt[3]{x} ), where “x” is the number we are taking the cube root of. For positive numbers, the cube root is also positive. Cube roots of negative numbers, however, will result in negative answers, because a negative number cubed will give a negative result. For example:
- ( \sqrt[3]{-27} = -3 ) because ( (-3)^3 = -27 ).
The cube root of a number is particularly useful in geometry, for example, when calculating the side length of a cube given its volume. If a cube has a volume of 216 cubic units, its side length would be the cube root of 216, which is 6 units.
Thus, the cube root of 216 is 6.