\left(\frac{4}{5\sqrt{60}}\right)\cdot\left(\sqrt{\frac{36}{48}}\right)

asked by guest
on Apr 06, 2025 at 4:13 pm



You asked:

Evaluate the expression: 45603648\frac{4}{5 \sqrt{60}} \sqrt{\frac{36}{48}}

MathBot Answer:

45603648=525≈0.08944271909999158785636694674925\frac{4}{5 \sqrt{60}} \sqrt{\frac{36}{48}} = \frac{\sqrt{5}}{25} \approx 0.08944271909999158785636694674925

45603648=4⋅15⋅60⋅3648=4⋅15⋅2⋅15⋅3648=4⋅110⋅15⋅3648=4⋅1150⋅15⋅3648=4⋅1150⋅15⋅12⋅3=275⋅15⋅12⋅3=125⋅5\begin{aligned}\frac{4}{5 \sqrt{60}} \sqrt{\frac{36}{48}}&=4 \cdot \frac{1}{5 \cdot \sqrt{60}} \cdot \sqrt{\frac{36}{48}}\\&=4 \cdot \frac{1}{5 \cdot 2 \cdot \sqrt{15}} \cdot \sqrt{\frac{36}{48}}\\&=4 \cdot \frac{1}{10 \cdot \sqrt{15}} \cdot \sqrt{\frac{36}{48}}\\&=4 \cdot \frac{1}{150} \cdot \sqrt{15} \cdot \sqrt{\frac{36}{48}}\\&=4 \cdot \frac{1}{150} \cdot \sqrt{15} \cdot \frac{1}{2} \cdot \sqrt{3}\\&=\frac{2}{75} \cdot \sqrt{15} \cdot \frac{1}{2} \cdot \sqrt{3}\\&=\frac{1}{25} \cdot \sqrt{5}\end{aligned}

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