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

asked by guest
on Apr 04, 2025 at 10:11 am



You asked:

Evaluate the expression: (35−42)(25+23)\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(2 \sqrt{5} + 2 \sqrt{3}\right)

MathBot Answer:

(35−42)(25+23)=(−42+35)(23+25)≈8.34376085363204186950617144558552\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(2 \sqrt{5} + 2 \sqrt{3}\right) = \left(- 4 \sqrt{2} + 3 \sqrt{5}\right) \left(2 \sqrt{3} + 2 \sqrt{5}\right) \approx 8.34376085363204186950617144558552

(35−42)(25+23)=(3⋅5−4⋅2)⋅(2⋅5+2⋅3)=(−4⋅2+3⋅5)⋅(2⋅5+2⋅3)=(−4⋅2+3⋅5)⋅(2⋅3+2⋅5)\begin{aligned}\left(3 \sqrt{5} - 4 \sqrt{2}\right) \left(2 \sqrt{5} + 2 \sqrt{3}\right)&=\left(3 \cdot \sqrt{5} - 4 \cdot \sqrt{2}\right) \cdot \left(2 \cdot \sqrt{5} + 2 \cdot \sqrt{3}\right)\\&=\left(-4 \cdot \sqrt{2} + 3 \cdot \sqrt{5}\right) \cdot \left(2 \cdot \sqrt{5} + 2 \cdot \sqrt{3}\right)\\&=\left(-4 \cdot \sqrt{2} + 3 \cdot \sqrt{5}\right) \cdot \left(2 \cdot \sqrt{3} + 2 \cdot \sqrt{5}\right)\end{aligned}

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