Basic Math Examples

\frac{\sqrt{20}}{\sqrt{60}}

$\frac{\sqrt{20}}{\sqrt{60}}$

Step 1

Combine

\sqrt{20}

$\sqrt{20}$ and

\sqrt{60}

$\sqrt{60}$ into a single radical.

\sqrt{\frac{20}{60}}

$\sqrt{\frac{20}{60}}$

Step 2

Cancel the common factor of

20

$20$ and

60

$60$ .

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Step 2.1

Factor

20

$20$ out of

20

$20$ .

\sqrt{\frac{20 (1)}{60}}

$\sqrt{\frac{20 (1)}{60}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

20

$20$ out of

60

$60$ .

\sqrt{\frac{20 \cdot 1}{20 \cdot 3}}

$\sqrt{\frac{20 \cdot 1}{20 \cdot 3}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{20 \cdot 1}{20 \cdot 3}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{1}{3}}$

$\sqrt{\frac{1}{3}}$

$\sqrt{\frac{1}{3}}$

Step 3

Rewrite

$\sqrt{\frac{1}{3}}$ as

$\frac{\sqrt{1}}{\sqrt{3}}$ .

$\frac{\sqrt{1}}{\sqrt{3}}$

Step 4

Any root of

$1$ is

$1$ .

$\frac{1}{\sqrt{3}}$

Step 5

Multiply

$\frac{1}{\sqrt{3}}$ by

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply

$\frac{1}{\sqrt{3}}$ by

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 6.2

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 6.3

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 6.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 6.5

Add

$1$ and

$1$ .

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

Step 6.6

Rewrite

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

$3$ .

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Step 6.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{3}$ as

$3^{\frac{1}{2}}$ .

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

Step 6.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.6.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 6.6.4

Cancel the common factor of

$2$ .

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Step 6.6.4.1

Cancel the common factor.

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

Step 6.6.4.2

Rewrite the expression.

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

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

Step 6.6.5

Evaluate the exponent.

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

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$