Question

algebra 1-23511200310d101
5-2: mathxl for school: additional practice
write the sum in its simplest form.
$4\sqrt{108} + \sqrt{27}$
$4\sqrt{108} + \sqrt{27} = \square$
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify \(\sqrt{108}\)

Factor 108: \(108 = 36\times3\), so \(\sqrt{108}=\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}=6\sqrt{3}\). Then \(4\sqrt{108}=4\times6\sqrt{3}=24\sqrt{3}\).

Step2: Simplify \(\sqrt{27}\)

Factor 27: \(27 = 9\times3\), so \(\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}\).

Step3: Add the simplified radicals

\(4\sqrt{108}+\sqrt{27}=24\sqrt{3}+3\sqrt{3}=(24 + 3)\sqrt{3}=27\sqrt{3}\).

Answer:

\(27\sqrt{3}\)