Algebra Examples

$\frac{\sqrt{15}}{3 \sqrt{6}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{6}$ into a single radical.

$\frac{\sqrt{\frac{15}{6}}}{3}$

Step 2

Cancel the common factor of $15$ and $6$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $15$ .

$\frac{\sqrt{\frac{3 (5)}{6}}}{3}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $3$ out of $6$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Rewrite $\sqrt{\frac{5}{2}}$ as $\frac{\sqrt{5}}{\sqrt{2}}$ .

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

Step 3.2

Multiply $\frac{\sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3.3

Combine and simplify the denominator.

Tap for more steps...

Step 3.3.1

Multiply $\frac{\sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3.3.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}}{3}$

Step 3.3.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}}{3}$

Step 3.3.4

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

$\frac{\frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}}{3}$

Step 3.3.5

Add $1$ and $1$ .

$\frac{\frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{2}}}{3}$

Step 3.3.6

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

Tap for more steps...

Step 3.3.6.1

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

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

Step 3.3.6.2

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

$\frac{\frac{\sqrt{5} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}}{3}$

Step 3.3.6.3

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

$\frac{\frac{\sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}}{3}$

Step 3.3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.6.4.1

Cancel the common factor.

$\frac{\frac{\sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}}{3}$

Step 3.3.6.4.2

Rewrite the expression.

$\frac{\frac{\sqrt{5} \sqrt{2}}{2^{1}}}{3}$

Step 3.3.6.5

Evaluate the exponent.

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

Step 3.4

Simplify the numerator.

Tap for more steps...

Step 3.4.1

Combine using the product rule for radicals.

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

Step 3.4.2

Multiply $5$ by $2$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Multiply $\frac{\sqrt{10}}{2} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 5.1

Multiply $\frac{\sqrt{10}}{2}$ by $\frac{1}{3}$ .

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

Step 5.2

Multiply $2$ by $3$ .

$\frac{\sqrt{10}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{6}$

Decimal Form:

$0.52704627 \dots$