find 3√27+3√0.008+3√0.064

asked by guest
on Nov 20, 2024 at 7:22 am



You asked:

Evaluate the expression: \(3 \cdot \sqrt{27} + 3 \cdot \sqrt{0.008} + 3 \cdot \sqrt{0.064}\)

MathBot Answer:

\[3 \cdot \sqrt{27} + 3 \cdot \sqrt{0.008} + 3 \cdot \sqrt{0.064} = \frac{3 \sqrt{5}}{25} + \frac{6 \sqrt{10}}{25} + 9 \sqrt{3} \approx 16.61573206386028144499585236446446\]

\[\begin{aligned}3 \cdot \sqrt{27} + 3 \cdot \sqrt{0.008} + 3 \cdot \sqrt{0.064}& = 3 \cdot \sqrt{27} + 3 \cdot \sqrt{\frac{8}{1000}} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 3 \cdot 3 \cdot \sqrt{3} + 3 \cdot \sqrt{\frac{8}{1000}} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 9 \cdot \sqrt{3} + 3 \cdot \sqrt{\frac{8}{1000}} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 9 \cdot \sqrt{3} + 3 \cdot \sqrt{\frac{1}{125}} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 9 \cdot \sqrt{3} + 3 \cdot \frac{1}{25} \cdot \sqrt{5} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5} + 3 \cdot \sqrt{\frac{64}{1000}}\\& = 9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5} + 3 \cdot \sqrt{\frac{8}{125}}\\& = 9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5} + 3 \cdot \frac{2}{25} \cdot \sqrt{10}\\& = 9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5} + \frac{6}{25} \cdot \sqrt{10}\\& = \left(9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5}\right) + \frac{6}{25} \cdot \sqrt{10}\\& = 9 \cdot \sqrt{3} + \frac{3}{25} \cdot \sqrt{5} + \frac{6}{25} \cdot \sqrt{10}\end{aligned}\]

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