Question

add or subtract as indicated.
$5\sqrt3{11} + 3\sqrt{11} - 6\sqrt{11}$

$5\sqrt3{11} + 3\sqrt{11} - 6\sqrt{11} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify like terms

Like terms are those with the same radical part. Here, \(3\sqrt{11}\) and \(-6\sqrt{11}\) are like terms (both have \(\sqrt{11}\)), while \(5\sqrt[3]{11}\) has a different radical (\(\sqrt[3]{11}\)) and can't be combined with the square root terms.

Step2: Combine like terms

For \(3\sqrt{11}-6\sqrt{11}\), factor out \(\sqrt{11}\): \((3 - 6)\sqrt{11}=-3\sqrt{11}\).

Step3: Write the final expression

Now, combine with the remaining term: \(5\sqrt[3]{11}-3\sqrt{11}\).

Answer:

\(5\sqrt[3]{11}-3\sqrt{11}\)