(7+2√50)(5-2√2)

asked by guest
on Nov 27, 2024 at 7:18 pm



You asked:

Evaluate the expression: (7+250)(5−22)\left(7 + 2 \sqrt{50}\right) \left(5 - 2 \sqrt{2}\right)

MathBot Answer:

(7+250)(5−22)=(5−22)(7+102)≈45.91168824543142175686079407154913\left(7 + 2 \sqrt{50}\right) \left(5 - 2 \sqrt{2}\right) = \left(5 - 2 \sqrt{2}\right) \left(7 + 10 \sqrt{2}\right) \approx 45.91168824543142175686079407154913

(7+250)(5−22)=(7+2⋅50)⋅(5−2⋅2)=(7+2⋅5⋅2)⋅(5−2⋅2)=(7+10⋅2)⋅(5−2⋅2)=(5−2⋅2)⋅(7+10⋅2)\begin{aligned}\left(7 + 2 \sqrt{50}\right) \left(5 - 2 \sqrt{2}\right)&=\left(7 + 2 \cdot \sqrt{50}\right) \cdot \left(5 - 2 \cdot \sqrt{2}\right)\\&=\left(7 + 2 \cdot 5 \cdot \sqrt{2}\right) \cdot \left(5 - 2 \cdot \sqrt{2}\right)\\&=\left(7 + 10 \cdot \sqrt{2}\right) \cdot \left(5 - 2 \cdot \sqrt{2}\right)\\&=\left(5 - 2 \cdot \sqrt{2}\right) \cdot \left(7 + 10 \cdot \sqrt{2}\right)\end{aligned}

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