Question

question 3 of 5

select the correct answer.

what is this expression in simplified form?

\\\sqrt3{6,000}\\

• \\(10 \sqrt3{6}\\)
• \\(6 \sqrt3{10}\\)
• \\(100 \sqrt3{6}\\)
• \\(3 \sqrt3{2,000}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Identify perfect cube factors

To simplify a cube root, look for the largest perfect cube that divides the number under the radical.

$$ 6,000 = 1,000 \times 6 $$

Since \(1,000 = 10^3\), it is a perfect cube.

Step 2: Apply the product property of radicals

Split the radical into the product of two separate cube roots:

$$ \sqrt[3]{6,000} = \sqrt[3]{1,000} \times \sqrt[3]{6} $$

Step 3: Simplify

Evaluate the cube root of the perfect cube:

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

Combine the terms:

$$ 10\sqrt[3]{6} $$

Answer:

\(10\sqrt[3]{6}\)