Solve for B 16=2 square root of 3*B

$16 = 2 \sqrt{3} \cdot B$

Step 1

Rewrite the equation as $2 \sqrt{3} \cdot B = 16$ .

$2 \sqrt{3} \cdot B = 16$

Step 2

Divide each term in $(2 \sqrt{3} \cdot B) = 16$ by $2 \sqrt{3}$ and simplify.

Divide each term in $(2 \sqrt{3} \cdot B) = 16$ by $2 \sqrt{3}$ .

$\frac{(2 \sqrt{3} \cdot B)}{2 \sqrt{3}} = \frac{16}{2 \sqrt{3}}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{3} \cdot B}{2 \sqrt{3}} = \frac{16}{2 \sqrt{3}}$

Rewrite the expression.

$\frac{\sqrt{3} \cdot B}{\sqrt{3}} = \frac{16}{2 \sqrt{3}}$

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

Cancel the common factor.

$\frac{\sqrt{3} \cdot B}{\sqrt{3}} = \frac{16}{2 \sqrt{3}}$

Divide $B$ by $1$ .

$B = \frac{16}{2 \sqrt{3}}$

Simplify the right side.

Cancel the common factor of $16$ and $2$ .

Factor $2$ out of $16$ .

$B = \frac{2 \cdot 8}{2 \sqrt{3}}$

Cancel the common factors.

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

$B = \frac{2 \cdot 8}{2 (\sqrt{3})}$

Cancel the common factor.

$B = \frac{2 \cdot 8}{2 \sqrt{3}}$

Rewrite the expression.

$B = \frac{8}{\sqrt{3}}$

Multiply $\frac{8}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$B = \frac{8}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{8}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$B = \frac{8 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

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

$B = \frac{8 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

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

$B = \frac{8 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$B = \frac{8 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$B = \frac{8 \sqrt{3}}{{\sqrt{3}}^{2}}$

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

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

$B = \frac{8 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$B = \frac{8 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$B = \frac{8 \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$B = \frac{8 \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$B = \frac{8 \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$B = \frac{8 \sqrt{3}}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$B = \frac{8 \sqrt{3}}{3}$

Decimal Form:

$B = 4.61880215 \dots$

Solve for B 16=2 square root of 3*B

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