\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: \(\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right)\)

MathBot Answer:

\[\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right) = - \frac{3 \sqrt{2}}{5} \approx -0.84852813742385702928101323452582\]

\[\begin{aligned}\frac{2}{\sqrt{5}} \cdot -\left( \frac{3}{\sqrt{10}} \right)& = 2 \cdot \frac{1}{\sqrt{5}} \cdot -1 \cdot 3 \cdot \frac{1}{\sqrt{10}}\\& = 2 \cdot \frac{1}{5} \cdot \sqrt{5} \cdot -1 \cdot 3 \cdot \frac{1}{\sqrt{10}}\\& = 2 \cdot \frac{1}{5} \cdot \sqrt{5} \cdot -1 \cdot \frac{3}{10} \cdot \sqrt{10}\\& = \frac{2}{5} \cdot \sqrt{5} \cdot -1 \cdot \frac{3}{10} \cdot \sqrt{10}\\& = - \frac{2}{5} \cdot \sqrt{5} \cdot \frac{3}{10} \cdot \sqrt{10}\\& = - \frac{3}{5} \cdot \sqrt{2}\end{aligned}\]

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