\frac{2}{\sqrt{5}}\cdot -\frac{3}{\sqrt{10}}

asked by berecocoheaidoo97
on Nov 26, 2024 at 8:24 am



You asked:

Evaluate the expression: 25⋅−(310)\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right)

MathBot Answer:

25⋅−(310)=−325≈−0.84852813742385702928101323452582\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right) = - \frac{3 \sqrt{2}}{5} \approx -0.84852813742385702928101323452582

25⋅−(310)=2⋅15⋅−1⋅3⋅110=2⋅15⋅5⋅−1⋅3⋅110=2⋅15⋅5⋅−1⋅310⋅10=25⋅5⋅−1⋅310⋅10=−25⋅5⋅310⋅10=−35⋅2\begin{aligned}\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right)&=2 \cdot \frac{1}{\sqrt{5}} \cdot -1 \cdot 3 \cdot \frac{1}{\sqrt{10}}\\&=2 \cdot \frac{1}{5} \cdot \sqrt{5} \cdot -1 \cdot 3 \cdot \frac{1}{\sqrt{10}}\\&=2 \cdot \frac{1}{5} \cdot \sqrt{5} \cdot -1 \cdot \frac{3}{10} \cdot \sqrt{10}\\&=\frac{2}{5} \cdot \sqrt{5} \cdot -1 \cdot \frac{3}{10} \cdot \sqrt{10}\\&=- \frac{2}{5} \cdot \sqrt{5} \cdot \frac{3}{10} \cdot \sqrt{10}\\&=- \frac{3}{5} \cdot \sqrt{2}\end{aligned}

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