Solve for I l=(2u)/(I^2)

$l = \frac{2 u}{I^{2}}$

Step 1

Rewrite the equation as $\frac{2 u}{I^{2}} = l$ .

$\frac{2 u}{I^{2}} = l$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$I^{2}, 1$

The LCM of one and any expression is the expression.

$I^{2}$

Step 3

Multiply each term in $\frac{2 u}{I^{2}} = l$ by $I^{2}$ to eliminate the fractions.

Multiply each term in $\frac{2 u}{I^{2}} = l$ by $I^{2}$ .

$\frac{2 u}{I^{2}} I^{2} = l I^{2}$

Simplify the left side.

Cancel the common factor of $I^{2}$ .

Cancel the common factor.

$\frac{2 u}{I^{2}} I^{2} = l I^{2}$

Rewrite the expression.

$2 u = l I^{2}$

Step 4

Solve the equation.

Rewrite the equation as $l I^{2} = 2 u$ .

$l I^{2} = 2 u$

Divide each term in $l I^{2} = 2 u$ by $l$ and simplify.

Divide each term in $l I^{2} = 2 u$ by $l$ .

$\frac{l I^{2}}{l} = \frac{2 u}{l}$

Simplify the left side.

Cancel the common factor of $l$ .

Cancel the common factor.

$\frac{l I^{2}}{l} = \frac{2 u}{l}$

Divide $I^{2}$ by $1$ .

$I^{2} = \frac{2 u}{l}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$I = \pm \sqrt{\frac{2 u}{l}}$

Simplify $\pm \sqrt{\frac{2 u}{l}}$ .

Rewrite $\sqrt{\frac{2 u}{l}}$ as $\frac{\sqrt{2 u}}{\sqrt{l}}$ .

$I = \pm \frac{\sqrt{2 u}}{\sqrt{l}}$

Multiply $\frac{\sqrt{2 u}}{\sqrt{l}}$ by $\frac{\sqrt{l}}{\sqrt{l}}$ .

$I = \pm \frac{\sqrt{2 u}}{\sqrt{l}} \cdot \frac{\sqrt{l}}{\sqrt{l}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{2 u}}{\sqrt{l}}$ by $\frac{\sqrt{l}}{\sqrt{l}}$ .

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{\sqrt{l} \sqrt{l}}$

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{{\sqrt{l}}^{1} \sqrt{l}}$

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{{\sqrt{l}}^{1} {\sqrt{l}}^{1}}$

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{{\sqrt{l}}^{1 + 1}}$

Add $1$ and $1$ .

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{{\sqrt{l}}^{2}}$

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

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{{(l^{\frac{1}{2}})}^{2}}$

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{l^{\frac{1}{2} \cdot 2}}$

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

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{l^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{l^{\frac{2}{2}}}$

Rewrite the expression.

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{l^{1}}$

Simplify.

$I = \pm \frac{\sqrt{2 u} \sqrt{l}}{l}$

Combine using the product rule for radicals.

$I = \pm \frac{\sqrt{2 u l}}{l}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$I = \frac{\sqrt{2 u l}}{l}$

Next, use the negative value of the $\pm$ to find the second solution.

$I = - \frac{\sqrt{2 u l}}{l}$

The complete solution is the result of both the positive and negative portions of the solution.

$I = \frac{\sqrt{2 u l}}{l}$

$I = - \frac{\sqrt{2 u l}}{l}$

$I = \frac{\sqrt{2 u l}}{l}$

$I = - \frac{\sqrt{2 u l}}{l}$

$I = \frac{\sqrt{2 u l}}{l}$

$I = - \frac{\sqrt{2 u l}}{l}$

Solve for I l=(2u)/(I^2)

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