which expression(s) is/are equivalent to \\(\\sqrt{72}\\)\na. \\(6\\sqrt{2}\\)\nb. \\(3\\sqrt{8}\\)\nc…

Explanation:

Step1: Simplify (\sqrt{72})

Factor 72: (72 = 36\times2), so (\sqrt{72}=\sqrt{36\times2}). By property (\sqrt{ab}=\sqrt{a}\times\sqrt{b}) ((a\geq0,b\geq0)), we get (\sqrt{36}\times\sqrt{2}=6\sqrt{2}), so A is equivalent.

Step2: Check Option B

Simplify (3\sqrt{8}). Factor 8: (8 = 4\times2), so (\sqrt{8}=\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}). Then (3\sqrt{8}=3\times2\sqrt{2}=6\sqrt{2}), which is equal to (\sqrt{72}), so B is equivalent.

Step3: Check Option C

Simplify (12\sqrt{3}). The value of (12\sqrt{3}\approx12\times1.732 = 20.784), and (\sqrt{72}\approx8.485), so they are not equal.

Step4: Check Option D

Simplify (2\sqrt{18}). Factor 18: (18 = 9\times2), so (\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}). Then (2\sqrt{18}=2\times3\sqrt{2}=6\sqrt{2}), which is equal to (\sqrt{72}), so D is equivalent.

Answer:

A. (6\sqrt{2}), B. (3\sqrt{8}), D. (2\sqrt{18})