Add or subtract as indicated and simplify.
$\sqrt[3]{50}+\sqrt[3]{8}-\sqrt[3]{18}$

• A. $\sqrt{40}$
• B. $\sqrt[3]{40}$
• C. $\sqrt[3]{40}+2$
• D. Not like radicals

Answer: (D)

Verified step by step guidance

1. Identify the cube roots given: \(\sqrt[3]{50} + \sqrt[3]{8} - \sqrt[3]{18}\). Our goal is to simplify each cube root as much as possible and then combine like terms if possible.
2. Start by factoring each radicand (the number inside the cube root) to find perfect cubes: - \$50 = 25 \times 2 = 5^2 \times 2$ - \$8 = 2^3\( (which is a perfect cube) - \)18 = 9 \times 2 = 3^2 \times 2$
3. Simplify the cube roots where possible: - \(\sqrt[3]{8} = 2\) because \$2^3 = 8$ - For \(\sqrt[3]{50}\) and \(\sqrt[3]{18}\), factor out any perfect cubes if possible. Since neither 50 nor 18 contains a perfect cube factor other than 1, they remain as cube roots.
4. Rewrite the expression with the simplified terms: \(\sqrt[3]{50} + 2 - \sqrt[3]{18}\)
5. Since \(\sqrt[3]{50}\) and \(\sqrt[3]{18}\) are not like radicals (they have different radicands), they cannot be combined further. The simplified expression is left as is.