3√7−2√28−5√63− 3√32−4√7+√175

asked by guest
on Oct 25, 2024 at 8:29 pm



You asked:

Evaluate the expression: \(3 \cdot \sqrt{7} - 2 \cdot \sqrt{28} - 5 \cdot \sqrt{63} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}\)

MathBot Answer:

\[3 \cdot \sqrt{7} - 2 \cdot \sqrt{28} - 5 \cdot \sqrt{63} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175} = - 15 \sqrt{7} - 12 \sqrt{2} \approx -56.65683241444599944314450099510528\]

\[\begin{aligned}3 \cdot \sqrt{7} - 2 \cdot \sqrt{28} - 5 \cdot \sqrt{63} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}& = 3 \cdot \sqrt{7} - 2 \cdot 2 \cdot \sqrt{7} - 5 \cdot \sqrt{63} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 5 \cdot \sqrt{63} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 5 \cdot 3 \cdot \sqrt{7} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 15 \cdot \sqrt{7} - 3 \cdot \sqrt{32} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 15 \cdot \sqrt{7} - 3 \cdot 4 \cdot \sqrt{2} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 15 \cdot \sqrt{7} - 12 \cdot \sqrt{2} - 4 \cdot \sqrt{7} + \sqrt{175}\\& = 3 \cdot \sqrt{7} - 4 \cdot \sqrt{7} - 15 \cdot \sqrt{7} - 12 \cdot \sqrt{2} - 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}\\& = - \sqrt{7} - 15 \cdot \sqrt{7} - 12 \cdot \sqrt{2} - 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}\\& = -16 \cdot \sqrt{7} - 12 \cdot \sqrt{2} - 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}\\& = \left(-16 \cdot \sqrt{7} - 12 \cdot \sqrt{2}\right) - 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}\\& = \left(-20 \cdot \sqrt{7} - 12 \cdot \sqrt{2}\right) + 5 \cdot \sqrt{7}\\& = -15 \cdot \sqrt{7} - 12 \cdot \sqrt{2}\end{aligned}\]

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