Basic Math Examples

$\sqrt{- \frac{16}{14} \cdot - 2}$

Step 1

Multiply $- 2$ by $- 1$ .

$\sqrt{2 (\frac{16}{14})}$

Step 2

Combine $2$ and $\frac{16}{14}$ .

$\sqrt{\frac{2 \cdot 16}{14}}$

Step 3

Reduce the expression $\frac{2 \cdot 16}{14}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $2 \cdot 16$ .

$\sqrt{\frac{2 (16)}{14}}$

Step 3.2

Factor $2$ out of $14$ .

$\sqrt{\frac{2 \cdot 16}{2 \cdot 7}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 16}{2 \cdot 7}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{16}{7}}$

Step 4

Rewrite $\sqrt{\frac{16}{7}}$ as $\frac{\sqrt{16}}{\sqrt{7}}$ .

$\frac{\sqrt{16}}{\sqrt{7}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{7}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{\sqrt{7}}$

Step 6

Multiply $\frac{4}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{4}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{4}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{4 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 7.2

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{4 \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 7.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{4 \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 7.4

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

$\frac{4 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 7.5

Add $1$ and $1$ .

$\frac{4 \sqrt{7}}{{\sqrt{7}}^{2}}$

Step 7.6

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

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{4 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

Step 7.6.2

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

$\frac{4 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 7.6.3

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

$\frac{4 \sqrt{7}}{7^{\frac{2}{2}}}$

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

$\frac{4 \sqrt{7}}{7^{\frac{2}{2}}}$

Step 7.6.4.2

Rewrite the expression.

$\frac{4 \sqrt{7}}{7^{1}}$

Step 7.6.5

Evaluate the exponent.

$\frac{4 \sqrt{7}}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{7}}{7}$

Decimal Form:

$1.51185789 \dots$