How do you simplify ³√3000?

To simplify the cube root of 3000, we first need to factor the number into its prime components.

Step 1: Factor 3000

We can break down 3000 as follows:

• 3000 = 3 × 1000
• 1000 = 10 × 100 = 10 × 10 × 10 = 10³
• 10 = 2 × 5

So, we can express 3000 as:

3000 = 3 × 2³ × 5³

Step 2: Apply the Cube Root

Now, we can find the cube root:

³√3000 = ³√(3 × 2³ × 5³)

This can be separated into:

³√3 × ³√(2³) × ³√(5³)

Step 3: Simplify Further

Since the cube root of a cube is the base itself, we have:

³√(2³) = 2 and ³√(5³) = 5

Thus, we can simplify it to:

³√3000 = 2 × 5 × ³√3

Final Result

Putting it all together, we find:

³√3000 = 10 × ³√3

This is the simplified form of the cube root of 3000.