Solve for I P=I^2R

$P = I^{2} R$

Rewrite the equation as $I^{2} R = P$ .

$I^{2} R = P$

Divide each term in $I^{2} R = P$ by $R$ and simplify.

Divide each term in $I^{2} R = P$ by $R$ .

$\frac{I^{2} R}{R} = \frac{P}{R}$

Simplify the left side.

Cancel the common factor of $R$ .

Cancel the common factor.

$\frac{I^{2} R}{R} = \frac{P}{R}$

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

$I^{2} = \frac{P}{R}$

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

$I = \pm \sqrt{\frac{P}{R}}$

Simplify $\pm \sqrt{\frac{P}{R}}$ .

Rewrite $\sqrt{\frac{P}{R}}$ as $\frac{\sqrt{P}}{\sqrt{R}}$ .

$I = \pm \frac{\sqrt{P}}{\sqrt{R}}$

Multiply $\frac{\sqrt{P}}{\sqrt{R}}$ by $\frac{\sqrt{R}}{\sqrt{R}}$ .

$I = \pm \frac{\sqrt{P}}{\sqrt{R}} \cdot \frac{\sqrt{R}}{\sqrt{R}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{P}}{\sqrt{R}}$ by $\frac{\sqrt{R}}{\sqrt{R}}$ .

$I = \pm \frac{\sqrt{P} \sqrt{R}}{\sqrt{R} \sqrt{R}}$

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{{\sqrt{R}}^{1} \sqrt{R}}$

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{{\sqrt{R}}^{1} {\sqrt{R}}^{1}}$

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{{\sqrt{R}}^{1 + 1}}$

Add $1$ and $1$ .

$I = \pm \frac{\sqrt{P} \sqrt{R}}{{\sqrt{R}}^{2}}$

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

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{{(R^{\frac{1}{2}})}^{2}}$

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{R^{\frac{1}{2} \cdot 2}}$

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

$I = \pm \frac{\sqrt{P} \sqrt{R}}{R^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$I = \pm \frac{\sqrt{P} \sqrt{R}}{R^{\frac{2}{2}}}$

Rewrite the expression.

$I = \pm \frac{\sqrt{P} \sqrt{R}}{R^{1}}$

Simplify.

$I = \pm \frac{\sqrt{P} \sqrt{R}}{R}$

Combine using the product rule for radicals.

$I = \pm \frac{\sqrt{P R}}{R}$

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.

$I = \frac{\sqrt{P R}}{R}$

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

$I = - \frac{\sqrt{P R}}{R}$

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

$I = \frac{\sqrt{P R}}{R}$

$I = - \frac{\sqrt{P R}}{R}$

$I = \frac{\sqrt{P R}}{R}$

$I = - \frac{\sqrt{P R}}{R}$

Solve for I P=I^2R

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