To simplify the expression \(2\sqrt{12} \times \sqrt{27} \times 2\sqrt{25}\), let's first break down each square root into its prime factors.
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Calculating the square roots:
- \(\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}\)
- \(\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}\)
- \(\sqrt{25} = \sqrt{5^2} = 5\)
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Substituting the simplified square roots back into the expression: \[ 2\sqrt{12} \times \sqrt{27} \times 2\sqrt{25} = 2(2\sqrt{3}) \times (3\sqrt{3}) \times 2(5) \] Let's also rearrange the constants and square roots: \[ = 2 \times 2 \times 2 \times 3 \times 5 \times \sqrt{3} \times \sqrt{3} \]
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Calculating the product of the constants: \[ 2 \times 2 \times 2 = 8 \] and, \[ 3 \times 5 = 15 \] So the constants multiply to: \[ 8 \times 15 = 120 \]
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Calculating the product of the square roots: \(\sqrt{3} \times \sqrt{3} = \sqrt{3^2} = 3\)
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Now, putting everything together: \[ 120 \times 3 = 360 \]
Thus, the final result in simplest radical form is: \[ \boxed{360} \]