Solve for b square root of b/5 = square root of 33-2b

$\sqrt{\frac{b}{5}} = \sqrt{33 - 2 b}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{b}{5}}}^{2} = {\sqrt{33 - 2 b}}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(\frac{b}{5})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{b}{5})}^{\frac{1}{2} \cdot 2} = {\sqrt{33 - 2 b}}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(\frac{b}{5})}^{\frac{1}{2} \cdot 2} = {\sqrt{33 - 2 b}}^{2}$

Rewrite the expression.

${(\frac{b}{5})}^{1} = {\sqrt{33 - 2 b}}^{2}$

Simplify.

$\frac{b}{5} = {\sqrt{33 - 2 b}}^{2}$

Rewrite ${\sqrt{33 - 2 b}}^{2}$ as $33 - 2 b$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{33 - 2 b}$ as ${(33 - 2 b)}^{\frac{1}{2}}$ .

$\frac{b}{5} = {({(33 - 2 b)}^{\frac{1}{2}})}^{2}$

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

$\frac{b}{5} = {(33 - 2 b)}^{\frac{1}{2} \cdot 2}$

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

$\frac{b}{5} = {(33 - 2 b)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{b}{5} = {(33 - 2 b)}^{\frac{2}{2}}$

Divide $1$ by $1$ .

$\frac{b}{5} = {(33 - 2 b)}^{1}$

Simplify.

$\frac{b}{5} = 33 - 2 b$

Solve for $b$ .

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Multiply both sides of the equation by $5$ .

$b = 33 \cdot (5) - 2 b \cdot 5$

Simplify each term.

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Multiply $33$ by $5$ .

$b = 165 - 2 b \cdot 5$

Multiply $5$ by $- 2$ .

$b = 165 - 10 b$

Move all terms containing $b$ to the left side of the equation.

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Add $10 b$ to both sides of the equation.

$b + 10 b = 165$

Add $b$ and $10 b$ .

$11 b = 165$

Divide each term by $11$ and simplify.

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Divide each term in $11 b = 165$ by $11$ .

$\frac{11 b}{11} = \frac{165}{11}$

Cancel the common factor of $11$ .

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Cancel the common factor.

$\frac{11 b}{11} = \frac{165}{11}$

Divide $b$ by $1$ .

$b = \frac{165}{11}$

Divide $165$ by $11$ .

$b = 15$

Solve for b square root of b/5 = square root of 33-2b

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