Cube Root

Change the number in the radical sign, 27,
to a cube.

Think of a number whose square is 27.
3 is good because 3³ = 27.

So ³√27 = ³√3³.

Cancel the cube root and the cube.
Then ³√3³ = 3.

Cube root and cube
are the opposite operations:
just like square and square root.

So you can cancel the cube root and the cube
like this.

So 3 is the answer.

Change the number in the radical sign, -8,
to a cube.

Think of a number whose cube is -8.
-2 is good because (-2)³ = -8.

So ³√-8 = ³√(-2)³.

Cancel the cube root and the cube.
Then ³√(-2)³ = -2.

So -2 is the answer.

Change the number in the radical sign, -1000,
to a cube.

Think of a number whose cube is -1000.
-10 is good because (-10)³ = -1000.

So -³√-1000 = -³√(-10)³.

Cancel the cube root and the cube.
Then -³√(-10)³ = -(-10).

-(-10) = 10

So -10 is the answer.