(3 5\sqrt{5} -4 2\sqrt{2} )(4 5\sqrt{5} +3 2\sqrt{2} )

asked by guest
on Apr 04, 2025 at 10:12 am



You asked:

Evaluate the expression: (35−42)(45+32)\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right)

MathBot Answer:

(35−42)(45+32)=(−42+35)(32+45)≈13.86405637882134467600774518897097\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right) = \left(- 4 \sqrt{2} + 3 \sqrt{5}\right) \left(3 \sqrt{2} + 4 \sqrt{5}\right) \approx 13.86405637882134467600774518897097

(35−42)(45+32)=(3⋅5−4⋅2)⋅(4⋅5+3⋅2)=(−4⋅2+3⋅5)⋅(4⋅5+3⋅2)=(−4⋅2+3⋅5)⋅(3⋅2+4⋅5)\begin{aligned}\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right)&=\left(3 \cdot \sqrt{5} - 4 \cdot \sqrt{2}\right) \cdot \left(4 \cdot \sqrt{5} + 3 \cdot \sqrt{2}\right)\\&=\left(-4 \cdot \sqrt{2} + 3 \cdot \sqrt{5}\right) \cdot \left(4 \cdot \sqrt{5} + 3 \cdot \sqrt{2}\right)\\&=\left(-4 \cdot \sqrt{2} + 3 \cdot \sqrt{5}\right) \cdot \left(3 \cdot \sqrt{2} + 4 \cdot \sqrt{5}\right)\end{aligned}

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