Algebra Examples

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 2.3

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 2.4

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

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

Step 2.5

Add $1$ and $1$ .

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

Step 2.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 2.6.2

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

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

Step 2.6.3

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

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

Step 2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.6.4.1

Cancel the common factor.

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

Step 2.6.4.2

Rewrite the expression.

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

Step 2.6.5

Evaluate the exponent.

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

Step 3

Multiply $\frac{10 \sqrt{3}}{3} \cdot 2$ .

Tap for more steps...

Step 3.1

Combine $\frac{10 \sqrt{3}}{3}$ and $2$ .

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

Step 3.2

Multiply $2$ by $10$ .

$\frac{20 \sqrt{3}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{20 \sqrt{3}}{3}$

Decimal Form:

$11.54700538 \dots$