Algebra Examples

$2.2 = 2 \cdot 3.14 \sqrt{\frac{L}{32}}$

Step 1

Rewrite the equation as $2 \cdot (3.14 \sqrt{\frac{L}{32}}) = 2.2$ .

$2 \cdot (3.14 \sqrt{\frac{L}{32}}) = 2.2$

Step 2

Multiply $3.14$ by $2$ .

$6.28 \cdot \sqrt{\frac{L}{32}} = 2.2$

Step 3

Divide each term in $6.28 \cdot \sqrt{\frac{L}{32}} = 2.2$ by $6.28$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $6.28 \cdot \sqrt{\frac{L}{32}} = 2.2$ by $6.28$ .

$\frac{6.28 \cdot \sqrt{\frac{L}{32}}}{6.28} = \frac{2.2}{6.28}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $6.28$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{6.28 \cdot \sqrt{\frac{L}{32}}}{6.28} = \frac{2.2}{6.28}$

Step 3.2.1.2

Divide $\sqrt{\frac{L}{32}}$ by $1$ .

$\sqrt{\frac{L}{32}} = \frac{2.2}{6.28}$

Step 3.2.2

Rewrite $\frac{L}{32}$ as ${(\frac{1}{4})}^{2} \frac{L}{2}$ .

Tap for more steps...

Step 3.2.2.1

Factor the perfect power $1^{2}$ out of $L$ .

$\sqrt{\frac{1^{2} L}{32}} = \frac{2.2}{6.28}$

Step 3.2.2.2

Factor the perfect power $4^{2}$ out of $32$ .

$\sqrt{\frac{1^{2} L}{4^{2} \cdot 2}} = \frac{2.2}{6.28}$

Step 3.2.2.3

Rearrange the fraction $\frac{1^{2} L}{4^{2} \cdot 2}$ .

$\sqrt{{(\frac{1}{4})}^{2} \frac{L}{2}} = \frac{2.2}{6.28}$

Step 3.2.3

Pull terms out from under the radical.

$\frac{1}{4} \sqrt{\frac{L}{2}} = \frac{2.2}{6.28}$

Step 3.2.4

Rewrite $\sqrt{\frac{L}{2}}$ as $\frac{\sqrt{L}}{\sqrt{2}}$ .

$\frac{1}{4} \cdot \frac{\sqrt{L}}{\sqrt{2}} = \frac{2.2}{6.28}$

Step 3.2.5

Multiply $\frac{\sqrt{L}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{1}{4} (\frac{\sqrt{L}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) = \frac{2.2}{6.28}$

Step 3.2.6

Combine and simplify the denominator.

Tap for more steps...

Step 3.2.6.1

Multiply $\frac{\sqrt{L}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{\sqrt{2} \sqrt{2}} = \frac{2.2}{6.28}$

Step 3.2.6.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} = \frac{2.2}{6.28}$

Step 3.2.6.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} = \frac{2.2}{6.28}$

Step 3.2.6.4

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

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{{\sqrt{2}}^{1 + 1}} = \frac{2.2}{6.28}$

Step 3.2.6.5

Add $1$ and $1$ .

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{{\sqrt{2}}^{2}} = \frac{2.2}{6.28}$

Step 3.2.6.6

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

Tap for more steps...

Step 3.2.6.6.1

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

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} = \frac{2.2}{6.28}$

Step 3.2.6.6.2

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

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}} = \frac{2.2}{6.28}$

Step 3.2.6.6.3

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

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{2^{\frac{2}{2}}} = \frac{2.2}{6.28}$

Step 3.2.6.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.6.6.4.1

Cancel the common factor.

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{2^{\frac{2}{2}}} = \frac{2.2}{6.28}$

Step 3.2.6.6.4.2

Rewrite the expression.

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{2^{1}} = \frac{2.2}{6.28}$

Step 3.2.6.6.5

Evaluate the exponent.

$\frac{1}{4} \cdot \frac{\sqrt{L} \sqrt{2}}{2} = \frac{2.2}{6.28}$

Step 3.2.7

Combine using the product rule for radicals.

$\frac{1}{4} \cdot \frac{\sqrt{L \cdot 2}}{2} = \frac{2.2}{6.28}$

Step 3.2.8

Multiply $\frac{1}{4} \cdot \frac{\sqrt{L \cdot 2}}{2}$ .

Tap for more steps...

Step 3.2.8.1

Multiply $\frac{1}{4}$ by $\frac{\sqrt{L \cdot 2}}{2}$ .

$\frac{\sqrt{L \cdot 2}}{4 \cdot 2} = \frac{2.2}{6.28}$

Step 3.2.8.2

Multiply $4$ by $2$ .

$\frac{\sqrt{L \cdot 2}}{8} = \frac{2.2}{6.28}$

Step 3.2.9

Reorder factors in $\frac{\sqrt{L \cdot 2}}{8}$ .

$\frac{\sqrt{2 L}}{8} = \frac{2.2}{6.28}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $2.2$ by $6.28$ .

$\frac{\sqrt{2 L}}{8} = 0.35031847$

Step 4

Multiply both sides by $8$ .

$\frac{\sqrt{2 L}}{8} \cdot 8 = 0.35031847 \cdot 8$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$\frac{\sqrt{2 L}}{8} \cdot 8 = 0.35031847 \cdot 8$

Step 5.1.1.2

Rewrite the expression.

$\sqrt{2 L} = 0.35031847 \cdot 8$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $0.35031847$ by $8$ .

$\sqrt{2 L} = 2.80254777$

Step 6

Solve for $L$ .

Tap for more steps...

Step 6.1

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

${\sqrt{2 L}}^{2} = {2.80254777}^{2}$

Step 6.2

Simplify each side of the equation.

Tap for more steps...

Step 6.2.1

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

${({(2 L)}^{\frac{1}{2}})}^{2} = {2.80254777}^{2}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

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

Tap for more steps...

Step 6.2.2.1.1

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

Tap for more steps...

Step 6.2.2.1.1.1

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

${(2 L)}^{\frac{1}{2} \cdot 2} = {2.80254777}^{2}$

Step 6.2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.2.1.1.2.1

Cancel the common factor.

${(2 L)}^{\frac{1}{2} \cdot 2} = {2.80254777}^{2}$

Step 6.2.2.1.1.2.2

Rewrite the expression.

${(2 L)}^{1} = {2.80254777}^{2}$

Step 6.2.2.1.2

Simplify.

$2 L = {2.80254777}^{2}$

Step 6.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.3.1

Raise $2.80254777$ to the power of $2$ .

$2 L = 7.854274$

Step 6.3

Divide each term in $2 L = 7.854274$ by $2$ and simplify.

Tap for more steps...

Step 6.3.1

Divide each term in $2 L = 7.854274$ by $2$ .

$\frac{2 L}{2} = \frac{7.854274}{2}$

Step 6.3.2

Simplify the left side.

Tap for more steps...

Step 6.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.3.2.1.1

Cancel the common factor.

$\frac{2 L}{2} = \frac{7.854274}{2}$

Step 6.3.2.1.2

Divide $L$ by $1$ .

$L = \frac{7.854274}{2}$

Step 6.3.3

Simplify the right side.

Tap for more steps...

Step 6.3.3.1

Divide $7.854274$ by $2$ .

$L = 3.927137$