Question

add or subtract.
$4\sqrt{27} - 2\sqrt{18} + \sqrt{75}$
$4\sqrt{27} - 2\sqrt{18} + \sqrt{75} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify each radical

Simplify \(4\sqrt{27}\): \(27 = 9\times3\), so \(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\), then \(4\sqrt{27}=4\times3\sqrt{3}=12\sqrt{3}\).
Simplify \(2\sqrt{18}\): \(18 = 9\times2\), so \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\), then \(2\sqrt{18}=2\times3\sqrt{2}=6\sqrt{2}\).
Simplify \(\sqrt{75}\): \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\).

Step2: Combine like radicals

Combine the \(\sqrt{3}\) terms: \(12\sqrt{3}+5\sqrt{3}=17\sqrt{3}\). The \(\sqrt{2}\) term \(-6\sqrt{2}\) remains as is since there are no other \(\sqrt{2}\) terms.

Answer:

\(17\sqrt{3} - 6\sqrt{2}\)