Evaluate:
(0.5)3×6×35\sqrt{(0.5)^3 \times 6 \times 3^5}(0.5)3×6×35
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(0.5)3×6×35=(510)3×6×35=(1251000)×6×243=(125500)×3×243=(25100)×729=(510)×27=(13510)=13.5\sqrt{(0.5)^3 \times 6 \times 3^5}\\[1em] = \sqrt{\Big(\dfrac{5}{10}\Big)^3 \times 6 \times 3^5}\\[1em] = \sqrt{\Big(\dfrac{125}{1000}\Big) \times 6 \times 243}\\[1em] = \sqrt{\Big(\dfrac{125}{500}\Big) \times 3 \times 243}\\[1em] = \sqrt{\Big(\dfrac{25}{100}\Big) \times 729}\\[1em] = \Big(\dfrac{5}{10}\Big) \times 27\\[1em] = \Big(\dfrac{135}{10}\Big)\\[1em] = 13.5(0.5)3×6×35=(105)3×6×35=(1000125)×6×243=(500125)×3×243=(10025)×729=(105)×27=(10135)=13.5
(0.5)3×6×35=13.5\sqrt{(0.5)^3 \times 6 \times 3^5} = 13.5(0.5)3×6×35=13.5
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