How Do you un Cube Something? Example: 5^3 = 125

How Do you un Cube Something? Example: 5^3 = 125

To “un-cube” something, you find the cube root of the number. For example, to un-cube 125 (5^3), you find the cube root of 125, which is 5. So, the cube root of 125 is 5 because 5 x 5 x 5 = 125. In mathematical notation, it’s represented as ∛125 = 5.

Finding Cube Roots to Undo Cubing

In mathematics, cubing a number involves raising it to the third power, indicating to multiply the number by itself three times. The cube root is the reverse operation, giving us back the original number before cubing it.

Let’s look at how to “uncube” 125 to get 5 step-by-step:

Understanding Cubes

Cubing means raising to the exponent 3. For example:

53 = 5 x 5 x 5 = 125

We multiplied 5 by itself 3 times. This gives the cubic result 125.

Cube Roots

The cube root “undoes” cubing a number. It asks what number cubed equals the given value. Symbolically, cube root is represented by a 3 in the radical:

3√125

This means “What number cubed is 125?”

Calculating the Cube Root

To evaluate 3√125:

1. Factor 125 into primes: 125 = 5 x 5 x 5
2. Since each prime occurs 3 times, the cube root is just one factor: 3√125 = 5

So the cube root of 125 is 5. This “uncubes” it back to the original number.

Checking Our Work

We can verify that uncubing 125 gives 5 by cubing 5 to see if we get 125 again:

53 = 5 x 5 x 5 = 125 ✅

Getting the original cubic number confirms that taking the cube root undid cubing correctly.

Understanding roots as the inverse of exponentiation reveals how to undo operations like cubing a number. Conceptualizing the processes builds algebra skills and helps connect related concepts.

In summary, to undo cubing a number, take the cube root. This reverses the original cubing by giving the number that was cubed to produce the cubic result.