Question

add or subtract.
$5\sqrt{75} - 3\sqrt{50} + \sqrt{48}$

$5\sqrt{75} - 3\sqrt{50} + \sqrt{48} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify each radical

Simplify \(5\sqrt{75}\): \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\), then \(5\sqrt{75}=5\times5\sqrt{3}=25\sqrt{3}\).
Simplify \(-3\sqrt{50}\): \(50 = 25\times2\), so \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\), then \(-3\sqrt{50}=-3\times5\sqrt{2}=-15\sqrt{2}\).
Simplify \(\sqrt{48}\): \(48 = 16\times3\), so \(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\).

Step2: Combine like - radical terms

Now we have \(25\sqrt{3}-15\sqrt{2}+4\sqrt{3}\). Combine the \(\sqrt{3}\) terms: \((25\sqrt{3}+4\sqrt{3})-15\sqrt{2}=29\sqrt{3}-15\sqrt{2}\).

Answer:

\(29\sqrt{3}-15\sqrt{2}\)