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

asked by guest
on Apr 04, 2025 at 10:14 am



You asked:

Evaluate the expression: (35−52)(45+32)\left(3 \sqrt{5} - 5 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right)

MathBot Answer:

(35−52)(45+32)=(−52+35)(32+45)≈−4.7850542618521726519878289887599\left(3 \sqrt{5} - 5 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right) = \left(- 5 \sqrt{2} + 3 \sqrt{5}\right) \left(3 \sqrt{2} + 4 \sqrt{5}\right) \approx -4.7850542618521726519878289887599

(35−52)(45+32)=(3⋅5−5⋅2)⋅(4⋅5+3⋅2)=(−5⋅2+3⋅5)⋅(4⋅5+3⋅2)=(−5⋅2+3⋅5)⋅(3⋅2+4⋅5)\begin{aligned}\left(3 \sqrt{5} - 5 \sqrt{2}\right) \left(4 \sqrt{5} + 3 \sqrt{2}\right)&=\left(3 \cdot \sqrt{5} - 5 \cdot \sqrt{2}\right) \cdot \left(4 \cdot \sqrt{5} + 3 \cdot \sqrt{2}\right)\\&=\left(-5 \cdot \sqrt{2} + 3 \cdot \sqrt{5}\right) \cdot \left(4 \cdot \sqrt{5} + 3 \cdot \sqrt{2}\right)\\&=\left(-5 \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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