Pre-Algebra Examples

$\frac{62}{\sqrt{6186}}$

Step 1

Multiply $\frac{62}{\sqrt{6186}}$ by $\frac{\sqrt{6186}}{\sqrt{6186}}$ .

$\frac{62}{\sqrt{6186}} \cdot \frac{\sqrt{6186}}{\sqrt{6186}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{62}{\sqrt{6186}}$ by $\frac{\sqrt{6186}}{\sqrt{6186}}$ .

$\frac{62 \sqrt{6186}}{\sqrt{6186} \sqrt{6186}}$

Step 2.2

Raise $\sqrt{6186}$ to the power of $1$ .

$\frac{62 \sqrt{6186}}{{\sqrt{6186}}^{1} \sqrt{6186}}$

Step 2.3

Raise $\sqrt{6186}$ to the power of $1$ .

$\frac{62 \sqrt{6186}}{{\sqrt{6186}}^{1} {\sqrt{6186}}^{1}}$

Step 2.4

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

$\frac{62 \sqrt{6186}}{{\sqrt{6186}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{62 \sqrt{6186}}{{\sqrt{6186}}^{2}}$

Step 2.6

Rewrite ${\sqrt{6186}}^{2}$ as $6186$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6186}$ as $6186^{\frac{1}{2}}$ .

$\frac{62 \sqrt{6186}}{{(6186^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$\frac{62 \sqrt{6186}}{6186^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$\frac{62 \sqrt{6186}}{6186^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{62 \sqrt{6186}}{6186^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{62 \sqrt{6186}}{6186^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{62 \sqrt{6186}}{6186}$

Step 3

Cancel the common factor of $62$ and $6186$ .

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Step 3.1

Factor $2$ out of $62 \sqrt{6186}$ .

$\frac{2 (31 \sqrt{6186})}{6186}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6186$ .

$\frac{2 (31 \sqrt{6186})}{2 (3093)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (31 \sqrt{6186})}{2 \cdot 3093}$

Step 3.2.3

Rewrite the expression.

$\frac{31 \sqrt{6186}}{3093}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{31 \sqrt{6186}}{3093}$

Decimal Form:

$0.78829129 \dots$