Basic Math Examples

$\frac{3 \sqrt{10}}{7 \sqrt{6}}$

Step 1

Combine $\sqrt{10}$ and $\sqrt{6}$ into a single radical.

$\frac{3 \sqrt{\frac{10}{6}}}{7}$

Step 2

Cancel the common factor of $10$ and $6$ .

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Step 2.1

Factor $2$ out of $10$ .

$\frac{3 \sqrt{\frac{2 (5)}{6}}}{7}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6$ .

$\frac{3 \sqrt{\frac{2 \cdot 5}{2 \cdot 3}}}{7}$

Step 2.2.2

Cancel the common factor.

$\frac{3 \sqrt{\frac{2 \cdot 5}{2 \cdot 3}}}{7}$

Step 2.2.3

Rewrite the expression.

$\frac{3 \sqrt{\frac{5}{3}}}{7}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt{\frac{5}{3}}$ as $\frac{\sqrt{5}}{\sqrt{3}}$ .

$\frac{3 \frac{\sqrt{5}}{\sqrt{3}}}{7}$

Step 3.2

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

$\frac{3 (\frac{\sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})}{7}$

Step 3.3

Combine and simplify the denominator.

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Step 3.3.1

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}}}{7}$

Step 3.3.2

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}}{7}$

Step 3.3.3

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}}{7}$

Step 3.3.4

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}}{7}$

Step 3.3.5

Add $1$ and $1$ .

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{{\sqrt{3}}^{2}}}{7}$

Step 3.3.6

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

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Step 3.3.6.1

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}}{7}$

Step 3.3.6.2

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}}{7}$

Step 3.3.6.3

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

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}}{7}$

Step 3.3.6.4

Cancel the common factor of $2$ .

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Step 3.3.6.4.1

Cancel the common factor.

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}}{7}$

Step 3.3.6.4.2

Rewrite the expression.

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{3^{1}}}{7}$

Step 3.3.6.5

Evaluate the exponent.

$\frac{3 \frac{\sqrt{5} \sqrt{3}}{3}}{7}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Combine using the product rule for radicals.

$\frac{3 \frac{\sqrt{5 \cdot 3}}{3}}{7}$

Step 3.4.2

Multiply $5$ by $3$ .

$\frac{3 \frac{\sqrt{15}}{3}}{7}$

Step 4

Combine $3$ and $\frac{\sqrt{15}}{3}$ .

$\frac{\frac{3 \sqrt{15}}{3}}{7}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Reduce the expression $\frac{3 \sqrt{15}}{3}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

$\frac{\frac{3 \sqrt{15}}{3}}{7}$

Step 5.1.2

Rewrite the expression.

$\frac{\frac{\sqrt{15}}{1}}{7}$

Step 5.2

Divide $\sqrt{15}$ by $1$ .

$\frac{\sqrt{15}}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{15}}{7}$

Decimal Form:

$0.55328333 \dots$