Question

use your understanding of perfect cubes to find the cube root.
type the correct answer in the box. use numerals instead of words.

\\\sqrt3{-1,000} = \\ \\

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Understand the cube root of a negative number

The cube root of a number \(x\), written as \(\sqrt[3]{x}\), is the value that, when multiplied by itself three times, equals \(x\).

Unlike square roots, taking the cube root of a negative number is possible and results in a negative number because:

$$ (\text{negative}) \times (\text{negative}) \times (\text{negative}) = \text{negative} $$

Step 2: Find the cube root of the magnitude

First, find the cube root of \(1,000\):

$$ 10 \times 10 \times 10 = 1,000 $$

$$ \sqrt[3]{1,000} = 10 $$

Step 3: Apply the negative sign

Since the radicand is \(-1,000\), we use the negative factor:

$$ (-10) \times (-10) \times (-10) = -1,000 $$

Therefore:

$$ \sqrt[3]{-1,000} = -10 $$

Answer:

-10