Questions: Which choices are equivalent to the expression below? Check all that apply. 3 √8 A. √6 ⋅ √12 B. √3 ⋅ √24 C. √3 ⋅ √12 D. 72 E. √9 ⋅ √8 F. √6 ⋅ √24

Solution Steps

To determine which choices are equivalent to the expression \(3 \sqrt{8}\), we need to simplify each option and compare it to the simplified form of \(3 \sqrt{8}\). Simplifying \(3 \sqrt{8}\) involves breaking down the radical and multiplying by the coefficient. For each option, simplify the product of radicals and check if it matches the simplified form of \(3 \sqrt{8}\).

The original expression is \(3 \sqrt{8}\). To simplify, we calculate: \[ 3 \sqrt{8} = 3 \times \sqrt{4 \times 2} = 3 \times 2 \sqrt{2} = 6 \sqrt{2} \] The numerical value of \(6 \sqrt{2}\) is approximately \(8.485\).

• Option A: \(\sqrt{6} \cdot \sqrt{12} = \sqrt{72} = 6 \sqrt{2}\), which is approximately \(8.485\).
• Option B: \(\sqrt{3} \cdot \sqrt{24} = \sqrt{72} = 6 \sqrt{2}\), which is approximately \(8.485\).
• Option C: \(\sqrt{3} \cdot \sqrt{12} = \sqrt{36} = 6\).
• Option D: \(72\).
• Option E: \(\sqrt{9} \cdot \sqrt{8} = 3 \cdot \sqrt{8} = 3 \times 2 \sqrt{2} = 6 \sqrt{2}\), which is approximately \(8.485\).
• Option F: \(\sqrt{6} \cdot \sqrt{24} = \sqrt{144} = 12\).

The simplified value of the original expression \(6 \sqrt{2}\) is approximately \(8.485\). Comparing this with the options:

• Options A, B, and E simplify to approximately \(8.485\), matching the original expression.

Final Answer