Evaluate (2 square root of 5)/(-3 square root of 50)

$\frac{2 \sqrt{5}}{- 3 \sqrt{50}}$

Step 1

Combine $\sqrt{5}$ and $\sqrt{50}$ into a single radical.

$\frac{2 \sqrt{\frac{5}{50}}}{- 3}$

Step 2

Cancel the common factor of $5$ and $50$ .

Factor $5$ out of $5$ .

$\frac{2 \sqrt{\frac{5 (1)}{50}}}{- 3}$

Cancel the common factors.

Factor $5$ out of $50$ .

$\frac{2 \sqrt{\frac{5 \cdot 1}{5 \cdot 10}}}{- 3}$

Cancel the common factor.

$\frac{2 \sqrt{\frac{5 \cdot 1}{5 \cdot 10}}}{- 3}$

Rewrite the expression.

$\frac{2 \sqrt{\frac{1}{10}}}{- 3}$

Step 3

Simplify the numerator.

Rewrite $\sqrt{\frac{1}{10}}$ as $\frac{\sqrt{1}}{\sqrt{10}}$ .

$\frac{2 \frac{\sqrt{1}}{\sqrt{10}}}{- 3}$

Any root of $1$ is $1$ .

$\frac{2 \frac{1}{\sqrt{10}}}{- 3}$

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{2 (\frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}})}{- 3}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{2 \frac{\sqrt{10}}{\sqrt{10} \sqrt{10}}}{- 3}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{2 \frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}}{- 3}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{2 \frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}}{- 3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 \frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}}{- 3}$

Add $1$ and $1$ .

$\frac{2 \frac{\sqrt{10}}{{\sqrt{10}}^{2}}}{- 3}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{2 \frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}}{- 3}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}}{- 3}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \frac{\sqrt{10}}{10^{\frac{2}{2}}}}{- 3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \frac{\sqrt{10}}{10^{\frac{2}{2}}}}{- 3}$

Rewrite the expression.

$\frac{2 \frac{\sqrt{10}}{10^{1}}}{- 3}$

Evaluate the exponent.

$\frac{2 \frac{\sqrt{10}}{10}}{- 3}$

Step 4

Simplify terms.

Combine $2$ and $\frac{\sqrt{10}}{10}$ .

$\frac{\frac{2 \sqrt{10}}{10}}{- 3}$

Reduce the expression $\frac{2 \sqrt{10}}{10}$ by cancelling the common factors.

Factor $2$ out of $2 \sqrt{10}$ .

$\frac{\frac{2 (\sqrt{10})}{10}}{- 3}$

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{\frac{\sqrt{10}}{5}}{- 3}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{10}}{5} \cdot \frac{1}{- 3}$

Step 6

Move the negative in front of the fraction.

$\frac{\sqrt{10}}{5} (- \frac{1}{3})$

Step 7

Multiply $\frac{\sqrt{10}}{5} (- \frac{1}{3})$ .

Multiply $\frac{\sqrt{10}}{5}$ by $\frac{1}{3}$ .

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

Multiply $5$ by $3$ .

$- \frac{\sqrt{10}}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{10}}{15}$

Decimal Form:

$- 0.21081851 \dots$

Evaluate (2 square root of 5)/(-3 square root of 50)

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