Basic Math Examples

$\frac{14 \sqrt{5}}{\sqrt{2}}$

Step 1

Multiply $\frac{14 \sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{14 \sqrt{5}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{14 \sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{14 \sqrt{5} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Step 2.2

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

$\frac{14 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Step 2.3

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

$\frac{14 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Step 2.4

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

$\frac{14 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{14 \sqrt{5} \sqrt{2}}{{\sqrt{2}}^{2}}$

Step 2.6

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

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Step 2.6.1

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

$\frac{14 \sqrt{5} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$\frac{14 \sqrt{5} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$\frac{14 \sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{14 \sqrt{5} \sqrt{2}}{2^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{14 \sqrt{5} \sqrt{2}}{2^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{14 \sqrt{5} \sqrt{2}}{2}$

Step 3

Cancel the common factor of $14$ and $2$ .

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Step 3.1

Factor $2$ out of $14 \sqrt{5} \sqrt{2}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{7 \sqrt{5} \sqrt{2}}{1}$

Step 3.2.4

Divide $7 \sqrt{5} \sqrt{2}$ by $1$ .

$7 \sqrt{5} \sqrt{2}$

Step 4

Multiply $7 \sqrt{5} \sqrt{2}$ .

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Step 4.1

Combine using the product rule for radicals.

$7 \sqrt{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$7 \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{10}$

Decimal Form:

$22.13594362 \dots$