Solve for b H = square root of 4b+f

$H = \sqrt{4 b + f}$

Rewrite the equation as $\sqrt{4 b + f} = H$ .

$\sqrt{4 b + f} = H$

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

${\sqrt{4 b + f}}^{2} = H^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 b + f}$ as ${(4 b + f)}^{\frac{1}{2}}$ .

${({(4 b + f)}^{\frac{1}{2}})}^{2} = H^{2}$

Simplify the left side.

Simplify ${({(4 b + f)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 b + f)}^{\frac{1}{2}})}^{2}$ .

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

${(4 b + f)}^{\frac{1}{2} \cdot 2} = H^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 b + f)}^{\frac{1}{2} \cdot 2} = H^{2}$

Rewrite the expression.

${(4 b + f)}^{1} = H^{2}$

Simplify.

$4 b + f = H^{2}$

Solve for $b$ .

Subtract $f$ from both sides of the equation.

$4 b = H^{2} - f$

Divide each term in $4 b = H^{2} - f$ by $4$ and simplify.

Divide each term in $4 b = H^{2} - f$ by $4$ .

$\frac{4 b}{4} = \frac{H^{2}}{4} + \frac{- f}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 b}{4} = \frac{H^{2}}{4} + \frac{- f}{4}$

Divide $b$ by $1$ .

$b = \frac{H^{2}}{4} + \frac{- f}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$b = \frac{H^{2}}{4} - \frac{f}{4}$