5√28+2√63-6√75

asked by guest
on Jan 19, 2025 at 7:00 am



You asked:

Evaluate the expression: \(5 \sqrt{28} + 2 \sqrt{63} - 6 \sqrt{75}\)

MathBot Answer:

\[5 \sqrt{28} + 2 \sqrt{63} - 6 \sqrt{75} = - 30 \sqrt{3} + 16 \sqrt{7} \approx -9.629503250032869357797538186948\]

\[\begin{aligned}5 \sqrt{28} + 2 \sqrt{63} - 6 \sqrt{75}& = 5 \cdot \sqrt{28} + 2 \cdot \sqrt{63} - 6 \cdot \sqrt{75}\\& = 5 \cdot 2 \cdot \sqrt{7} + 2 \cdot \sqrt{63} - 6 \cdot \sqrt{75}\\& = 10 \cdot \sqrt{7} + 2 \cdot \sqrt{63} - 6 \cdot \sqrt{75}\\& = 10 \cdot \sqrt{7} + 2 \cdot 3 \cdot \sqrt{7} - 6 \cdot \sqrt{75}\\& = 10 \cdot \sqrt{7} + 6 \cdot \sqrt{7} - 6 \cdot \sqrt{75}\\& = 10 \cdot \sqrt{7} + 6 \cdot \sqrt{7} - 6 \cdot 5 \cdot \sqrt{3}\\& = 10 \cdot \sqrt{7} + 6 \cdot \sqrt{7} - 30 \cdot \sqrt{3}\\& = 16 \cdot \sqrt{7} - 30 \cdot \sqrt{3}\\& = -30 \cdot \sqrt{3} + 16 \cdot \sqrt{7}\end{aligned}\]

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