\(6\sqrt[2]{8}-8\sqrt[2]{2}+10\sqrt[2]{4}-4\sqrt[2]{16}\)

asked by guest
on Oct 05, 2024 at 11:27 pm



You asked:

Evaluate the expression: \(6 \cdot \sqrt[2]{8} - 8 \cdot \sqrt[2]{2} + 10 \cdot \sqrt[2]{4} - 4 \cdot \sqrt[2]{16}\)

MathBot Answer:

\[6 \cdot \sqrt[2]{8} - 8 \cdot \sqrt[2]{2} + 10 \cdot \sqrt[2]{4} - 4 \cdot \sqrt[2]{16} = 4 + 4 \sqrt{2} \approx 9.65685424949238019520675489683879\]

\[\begin{aligned}6 \cdot \sqrt[2]{8} - 8 \cdot \sqrt[2]{2} + 10 \cdot \sqrt[2]{4} - 4 \cdot \sqrt[2]{16}& = 6 \cdot \sqrt{8} - 8 \cdot \sqrt{2} + 10 \cdot \sqrt{4} - 4 \cdot \sqrt{16}\\& = 6 \cdot 2 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 10 \cdot \sqrt{4} - 4 \cdot \sqrt{16}\\& = 12 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 10 \cdot \sqrt{4} - 4 \cdot \sqrt{16}\\& = 12 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 10 \cdot 2 - 4 \cdot \sqrt{16}\\& = 12 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 20 - 4 \cdot \sqrt{16}\\& = 12 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 20 - 4 \cdot 4\\& = 12 \cdot \sqrt{2} - 8 \cdot \sqrt{2} + 20 - 16\\& = 4 \cdot \sqrt{2} + 20 - 16\\& = \left(20 + 4 \cdot \sqrt{2}\right) - 16\\& = 4 + 4 \cdot \sqrt{2}\end{aligned}\]

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