$\sqrt{75}$ - 2 $\sqrt{12}$ + 5 $\sqrt{27}$

asked by guest
on Sep 23, 2024 at 9:18 am



You asked:

Evaluate the expression: \(\sqrt{75} - 2 \cdot \sqrt{12} + 5 \cdot \sqrt{27}\)

MathBot Answer:

\[\sqrt{75} - 2 \cdot \sqrt{12} + 5 \cdot \sqrt{27} = 16 \sqrt{3} \approx 27.71281292110203669643914146409396\]

\[\begin{aligned}\sqrt{75} - 2 \cdot \sqrt{12} + 5 \cdot \sqrt{27}& = 5 \cdot \sqrt{3} - 2 \cdot \sqrt{12} + 5 \cdot \sqrt{27}\\& = 5 \cdot \sqrt{3} - 2 \cdot 2 \cdot \sqrt{3} + 5 \cdot \sqrt{27}\\& = 5 \cdot \sqrt{3} - 4 \cdot \sqrt{3} + 5 \cdot \sqrt{27}\\& = 5 \cdot \sqrt{3} - 4 \cdot \sqrt{3} + 5 \cdot 3 \cdot \sqrt{3}\\& = 5 \cdot \sqrt{3} - 4 \cdot \sqrt{3} + 15 \cdot \sqrt{3}\\& = \sqrt{3} + 15 \cdot \sqrt{3}\\& = 16 \cdot \sqrt{3}\end{aligned}\]

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