Basic Math Examples

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

Step 1

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

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

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{b}{5}}$ as ${(\frac{b}{5})}^{\frac{1}{2}}$ .

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(\frac{b}{5})}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

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

Tap for more steps...

Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Simplify.

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

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

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

Tap for more steps...

Step 2.3.1.1

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

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

Step 2.3.1.2

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

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

Step 2.3.1.3

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

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

Step 2.3.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.4.1

Cancel the common factor.

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

Step 2.3.1.4.2

Rewrite the expression.

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

Step 2.3.1.5

Simplify.

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

Step 3

Solve for $b$ .

Tap for more steps...

Step 3.1

Multiply both sides by $5$ .

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

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.1.1.1

Cancel the common factor.

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

Step 3.2.1.1.2

Rewrite the expression.

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

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Simplify $(33 - 2 b) \cdot 5$ .

Tap for more steps...

Step 3.2.2.1.1

Apply the distributive property.

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

Step 3.2.2.1.2

Simplify the expression.

Tap for more steps...

Step 3.2.2.1.2.1

Multiply $33$ by $5$ .

$b = 165 - 2 b \cdot 5$

Step 3.2.2.1.2.2

Multiply $5$ by $- 2$ .

$b = 165 - 10 b$

Step 3.2.2.1.2.3

Reorder $165$ and $- 10 b$ .

$b = - 10 b + 165$

Step 3.3

Solve for $b$ .

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

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

$b + 10 b = 165$

Step 3.3.1.2

Add $b$ and $10 b$ .

$11 b = 165$

Step 3.3.2

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

Tap for more steps...

Step 3.3.2.1

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

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

Step 3.3.2.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 3.3.2.2.1.1

Cancel the common factor.

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

Step 3.3.2.2.1.2

Divide $b$ by $1$ .

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

Step 3.3.2.3

Simplify the right side.

Tap for more steps...

Step 3.3.2.3.1

Divide $165$ by $11$ .

$b = 15$