Question

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

Explanation:

Step1: Identify like terms

Like terms for radicals have the same index and radicand. Here, the target is \(9\sqrt[3]{10}\), so we need terms with \(\sqrt[3]{10}\).

Step2: Analyze each option

• First option: \(5\sqrt[3]{10}+4\sqrt{10}\) – different radicals (\(\sqrt[3]{10}\) and \(\sqrt{10}\)), can't combine.
• Second option: \(5\sqrt[3]{10}+4\sqrt[3]{10}\) – combine like terms: \((5 + 4)\sqrt[3]{10}=9\sqrt[3]{10}\).
• Third option: \(5\sqrt{10}+4\sqrt[3]{10}\) – different radicals, can't combine.
• Fourth option: \(5\sqrt{10}+4\sqrt{10}\) – combines to \(9\sqrt{10}\), not \(9\sqrt[3]{10}\).

Answer:

The second option: \(5\sqrt[3]{10}+4\sqrt[3]{10}\)