Question

which expression equals $9sqrt3{10}$?
$\circ$ $5sqrt{10} + 4sqrt{10}$
$\circ$ $5sqrt3{10} + 4sqrt3{10}$
$\circ$ $5sqrt{10} + 4sqrt3{10}$
$\circ$ $5sqrt3{10} + 4sqrt{10}$

Explanation:

Step1: Analyze like radicals

Like radicals have the same root and radicand. Here, we need terms with $\sqrt[3]{10}$.

Step2: Combine like terms

For the option $5\sqrt[3]{10}+4\sqrt[3]{10}$, factor out $\sqrt[3]{10}$:
$\sqrt[3]{10}(5+4) = 9\sqrt[3]{10}$

Step3: Eliminate other options

• $5\sqrt{10}+4\sqrt{10}=9\sqrt{10}$ (not $\sqrt[3]{10}$)
• $5\sqrt{10}+4\sqrt[3]{10}$: unlike radicals, cannot combine to $9\sqrt[3]{10}$
• $5\sqrt[3]{10}+4\sqrt{10}$: unlike radicals, cannot combine to $9\sqrt[3]{10}$

Answer:

B. $5\sqrt[3]{10}+4\sqrt[3]{10}$