(3√5+2√3)(√5−4√3)

asked by guest
on Mar 18, 2025 at 6:18 am



You asked:

Evaluate the expression: (35+23)(5−43)\left(3 \sqrt{5} + 2 \sqrt{3}\right) \left(\sqrt{5} - 4 \sqrt{3}\right)

MathBot Answer:

(35+23)(5−43)=(−43+5)(23+35)≈−47.729833462074168851792653997824\left(3 \sqrt{5} + 2 \sqrt{3}\right) \left(\sqrt{5} - 4 \sqrt{3}\right) = \left(- 4 \sqrt{3} + \sqrt{5}\right) \left(2 \sqrt{3} + 3 \sqrt{5}\right) \approx -47.729833462074168851792653997824

(35+23)(5−43)=(3⋅5+2⋅3)⋅(5−4⋅3)=(2⋅3+3⋅5)⋅(5−4⋅3)=(5−4⋅3)⋅(2⋅3+3⋅5)\begin{aligned}\left(3 \sqrt{5} + 2 \sqrt{3}\right) \left(\sqrt{5} - 4 \sqrt{3}\right)&=\left(3 \cdot \sqrt{5} + 2 \cdot \sqrt{3}\right) \cdot \left(\sqrt{5} - 4 \cdot \sqrt{3}\right)\\&=\left(2 \cdot \sqrt{3} + 3 \cdot \sqrt{5}\right) \cdot \left(\sqrt{5} - 4 \cdot \sqrt{3}\right)\\&=\left(\sqrt{5} - 4 \cdot \sqrt{3}\right) \cdot \left(2 \cdot \sqrt{3} + 3 \cdot \sqrt{5}\right)\end{aligned}

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