Solve for m m/( square root of 3)-11=4

$\frac{m}{\sqrt{3}} - 11 = 4$

Step 1

Simplify each term.

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

$\frac{m}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} - 11 = 4$

Combine and simplify the denominator.

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

$\frac{m \sqrt{3}}{\sqrt{3} \sqrt{3}} - 11 = 4$

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

$\frac{m \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} - 11 = 4$

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

$\frac{m \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} - 11 = 4$

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

$\frac{m \sqrt{3}}{{\sqrt{3}}^{1 + 1}} - 11 = 4$

Add $1$ and $1$ .

$\frac{m \sqrt{3}}{{\sqrt{3}}^{2}} - 11 = 4$

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

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

$\frac{m \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} - 11 = 4$

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

$\frac{m \sqrt{3}}{3^{\frac{1}{2} \cdot 2}} - 11 = 4$

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

$\frac{m \sqrt{3}}{3^{\frac{2}{2}}} - 11 = 4$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{m \sqrt{3}}{3^{\frac{2}{2}}} - 11 = 4$

Rewrite the expression.

$\frac{m \sqrt{3}}{3^{1}} - 11 = 4$

Evaluate the exponent.

$\frac{m \sqrt{3}}{3} - 11 = 4$

Step 2

Move all terms not containing $m$ to the right side of the equation.

Add $11$ to both sides of the equation.

$\frac{m \sqrt{3}}{3} = 4 + 11$

Add $4$ and $11$ .

$\frac{m \sqrt{3}}{3} = 15$

Step 3

Multiply both sides of the equation by $\frac{3}{\sqrt{3}}$ .

$\frac{3}{\sqrt{3}} \cdot \frac{m \sqrt{3}}{3} = \frac{3}{\sqrt{3}} \cdot 15$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{\sqrt{3}} \cdot \frac{m \sqrt{3}}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{\sqrt{3}} \cdot \frac{m \sqrt{3}}{3} = \frac{3}{\sqrt{3}} \cdot 15$

Rewrite the expression.

$\frac{1}{\sqrt{3}} (m \sqrt{3}) = \frac{3}{\sqrt{3}} \cdot 15$

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

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

$\frac{1}{\sqrt{3}} (\sqrt{3} m) = \frac{3}{\sqrt{3}} \cdot 15$

Cancel the common factor.

$\frac{1}{\sqrt{3}} (\sqrt{3} m) = \frac{3}{\sqrt{3}} \cdot 15$

Rewrite the expression.

$m = \frac{3}{\sqrt{3}} \cdot 15$

Simplify the right side.

Simplify $\frac{3}{\sqrt{3}} \cdot 15$ .

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

$m = \frac{3}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \cdot 15$

Combine and simplify the denominator.

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

$m = \frac{3 \sqrt{3}}{\sqrt{3} \sqrt{3}} \cdot 15$

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

$m = \frac{3 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \cdot 15$

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

$m = \frac{3 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \cdot 15$

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

$m = \frac{3 \sqrt{3}}{{\sqrt{3}}^{1 + 1}} \cdot 15$

Add $1$ and $1$ .

$m = \frac{3 \sqrt{3}}{{\sqrt{3}}^{2}} \cdot 15$

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

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

$m = \frac{3 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \cdot 15$

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

$m = \frac{3 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \cdot 15$

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

$m = \frac{3 \sqrt{3}}{3^{\frac{2}{2}}} \cdot 15$

Cancel the common factor of $2$ .

Cancel the common factor.

$m = \frac{3 \sqrt{3}}{3^{\frac{2}{2}}} \cdot 15$

Rewrite the expression.

$m = \frac{3 \sqrt{3}}{3^{1}} \cdot 15$

Evaluate the exponent.

$m = \frac{3 \sqrt{3}}{3} \cdot 15$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$m = \frac{3 \sqrt{3}}{3} \cdot (3 (5))$

Cancel the common factor.

$m = \frac{3 \sqrt{3}}{3} \cdot (3 \cdot 5)$

Rewrite the expression.

$m = 3 \sqrt{3} \cdot 5$

Multiply $5$ by $3$ .

$m = 15 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = 15 \sqrt{3}$

Decimal Form:

$m = 25.98076211 \dots$

Solve for m m/( square root of 3)-11=4

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