Basic Math Examples

$72 = k (\sqrt{3}) (2)$

Step 1

Rewrite the equation as $k (\sqrt{3}) \cdot 2 = 72$ .

$k (\sqrt{3}) \cdot 2 = 72$

Step 2

Divide each term in $k (\sqrt{3}) \cdot 2 = 72$ by $2 \sqrt{3}$ and simplify.

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Step 2.1

Divide each term in $k (\sqrt{3}) \cdot 2 = 72$ by $2 \sqrt{3}$ .

$\frac{k \sqrt{3} \cdot 2}{2 \sqrt{3}} = \frac{72}{2 \sqrt{3}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sqrt{3}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{k \sqrt{3} \cdot 2}{2 \sqrt{3}} = \frac{72}{2 \sqrt{3}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{k \cdot 2}{2} = \frac{72}{2 \sqrt{3}}$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{k \cdot 2}{2} = \frac{72}{2 \sqrt{3}}$

Step 2.2.2.2

Divide $k$ by $1$ .

$k = \frac{72}{2 \sqrt{3}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $72$ and $2$ .

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Step 2.3.1.1

Factor $2$ out of $72$ .

$k = \frac{2 \cdot 36}{2 \sqrt{3}}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $2 \sqrt{3}$ .

$k = \frac{2 \cdot 36}{2 (\sqrt{3})}$

Step 2.3.1.2.2

Cancel the common factor.

$k = \frac{2 \cdot 36}{2 \sqrt{3}}$

Step 2.3.1.2.3

Rewrite the expression.

$k = \frac{36}{\sqrt{3}}$

Step 2.3.2

Multiply $\frac{36}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$k = \frac{36}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 2.3.3

Combine and simplify the denominator.

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Step 2.3.3.1

Multiply $\frac{36}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$k = \frac{36 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 2.3.3.2

Raise $\sqrt{3}$ to the power of $1$ .

$k = \frac{36 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 2.3.3.3

Raise $\sqrt{3}$ to the power of $1$ .

$k = \frac{36 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 2.3.3.4

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

$k = \frac{36 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 2.3.3.5

Add $1$ and $1$ .

$k = \frac{36 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 2.3.3.6

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

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Step 2.3.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$k = \frac{36 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 2.3.3.6.2

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

$k = \frac{36 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 2.3.3.6.3

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

$k = \frac{36 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 2.3.3.6.4

Cancel the common factor of $2$ .

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Step 2.3.3.6.4.1

Cancel the common factor.

$k = \frac{36 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 2.3.3.6.4.2

Rewrite the expression.

$k = \frac{36 \sqrt{3}}{3^{1}}$

Step 2.3.3.6.5

Evaluate the exponent.

$k = \frac{36 \sqrt{3}}{3}$

Step 2.3.4

Cancel the common factor of $36$ and $3$ .

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Step 2.3.4.1

Factor $3$ out of $36 \sqrt{3}$ .

$k = \frac{3 (12 \sqrt{3})}{3}$

Step 2.3.4.2

Cancel the common factors.

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Step 2.3.4.2.1

Factor $3$ out of $3$ .

$k = \frac{3 (12 \sqrt{3})}{3 (1)}$

Step 2.3.4.2.2

Cancel the common factor.

$k = \frac{3 (12 \sqrt{3})}{3 \cdot 1}$

Step 2.3.4.2.3

Rewrite the expression.

$k = \frac{12 \sqrt{3}}{1}$

Step 2.3.4.2.4

Divide $12 \sqrt{3}$ by $1$ .

$k = 12 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = 12 \sqrt{3}$

Decimal Form:

$k = 20.78460969 \dots$