Basic Math Examples

$\frac{9}{\sqrt{28}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite

$28$ as

$2^{2} \cdot 7$ .

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Step 1.1.1

Factor

$4$ out of

$28$ .

$\frac{9}{\sqrt{4 (7)}}$

Step 1.1.2

Rewrite

$4$ as

$2^{2}$ .

$\frac{9}{\sqrt{2^{2} \cdot 7}}$

$\frac{9}{\sqrt{2^{2} \cdot 7}}$

Step 1.2

Pull terms out from under the radical.

$\frac{9}{2 \sqrt{7}}$

$\frac{9}{2 \sqrt{7}}$

Step 2

Multiply

$\frac{9}{2 \sqrt{7}}$ by

$\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{9}{2 \sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

$\frac{9}{2 \sqrt{7}}$ by

$\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{9 \sqrt{7}}{2 \sqrt{7} \sqrt{7}}$

Step 3.2

Move

$\sqrt{7}$ .

$\frac{9 \sqrt{7}}{2 (\sqrt{7} \sqrt{7})}$

Step 3.3

Raise

$\sqrt{7}$ to the power of

$1$ .

$\frac{9 \sqrt{7}}{2 ({\sqrt{7}}^{1} \sqrt{7})}$

Step 3.4

Raise

$\sqrt{7}$ to the power of

$1$ .

$\frac{9 \sqrt{7}}{2 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}$

Step 3.5

Use the power rule

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

$\frac{9 \sqrt{7}}{2 {\sqrt{7}}^{1 + 1}}$

Step 3.6

Add

$1$ and

$1$ .

$\frac{9 \sqrt{7}}{2 {\sqrt{7}}^{2}}$

Step 3.7

Rewrite

${\sqrt{7}}^{2}$ as

$7$ .

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Step 3.7.1

Use

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

$\sqrt{7}$ as

$7^{\frac{1}{2}}$ .

$\frac{9 \sqrt{7}}{2 {(7^{\frac{1}{2}})}^{2}}$

Step 3.7.2

Apply the power rule and multiply exponents,

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

$\frac{9 \sqrt{7}}{2 \cdot 7^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{9 \sqrt{7}}{2 \cdot 7^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of

$2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{9 \sqrt{7}}{2 \cdot 7^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{9 \sqrt{7}}{2 \cdot 7^{1}}$

$\frac{9 \sqrt{7}}{2 \cdot 7^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{9 \sqrt{7}}{2 \cdot 7}$

$\frac{9 \sqrt{7}}{2 \cdot 7}$

$\frac{9 \sqrt{7}}{2 \cdot 7}$

Step 4

Multiply

$2$ by

$7$ .

$\frac{9 \sqrt{7}}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9 \sqrt{7}}{14}$

Decimal Form:

$1.70084012 \dots$

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