Solve for h D(h)=111.7 square root of h

$D (h) = 111.7 \sqrt{h}$

Rewrite the equation as $111.7 \sqrt{h} = D h$ .

$111.7 \sqrt{h} = D h$

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

${(111.7 \sqrt{h})}^{2} = {(D h)}^{2}$

Simplify each side of the equation.

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

${(111.7 h^{\frac{1}{2}})}^{2} = {(D h)}^{2}$

Simplify the left side.

Simplify ${(111.7 h^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $111.7 h^{\frac{1}{2}}$ .

${111.7}^{2} {(h^{\frac{1}{2}})}^{2} = {(D h)}^{2}$

Raise $111.7$ to the power of $2$ .

$12476.89 {(h^{\frac{1}{2}})}^{2} = {(D h)}^{2}$

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

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

$12476.89 h^{\frac{1}{2} \cdot 2} = {(D h)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12476.89 h^{\frac{1}{2} \cdot 2} = {(D h)}^{2}$

Rewrite the expression.

$12476.89 h^{1} = {(D h)}^{2}$

Simplify.

$12476.89 h = {(D h)}^{2}$

Simplify the right side.

Apply the product rule to $D h$ .

$12476.89 h = D^{2} h^{2}$

Solve for $h$ .

Subtract $D^{2} h^{2}$ from both sides of the equation.

$12476.89 h - D^{2} h^{2} = 0$

Factor $0.01 h$ out of $12476.89 h - D^{2} h^{2}$ .

Move $D^{2}$ .

$12476.89 h - 1 h^{2} D^{2} = 0$

Factor $0.01 h$ out of $12476.89 h$ .

$0.01 h (1247689) - 1 h^{2} D^{2} = 0$

Factor $0.01 h$ out of $- 1 h^{2} D^{2}$ .

$0.01 h (1247689) + 0.01 h (- 100 h D^{2}) = 0$

Factor $0.01 h$ out of $0.01 h (1247689) + 0.01 h (- 100 h D^{2})$ .

$0.01 h (1247689 - 100 h D^{2}) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$h = 0$

$1247689 - 100 h D^{2} = 0$

Set $h$ equal to $0$ .

$h = 0$

Set $1247689 - 100 h D^{2}$ equal to $0$ and solve for $h$ .

Set $1247689 - 100 h D^{2}$ equal to $0$ .

$1247689 - 100 h D^{2} = 0$

Solve $1247689 - 100 h D^{2} = 0$ for $h$ .

Subtract $1247689$ from both sides of the equation.

$- 100 h D^{2} = - 1247689$

Divide each term in $- 100 h D^{2} = - 1247689$ by $- 100 D^{2}$ and simplify.

Divide each term in $- 100 h D^{2} = - 1247689$ by $- 100 D^{2}$ .

$\frac{- 100 h D^{2}}{- 100 D^{2}} = \frac{- 1247689}{- 100 D^{2}}$

Simplify the left side.

Cancel the common factor of $- 100$ .

Cancel the common factor.

$\frac{- 100 h D^{2}}{- 100 D^{2}} = \frac{- 1247689}{- 100 D^{2}}$

Rewrite the expression.

$\frac{h D^{2}}{D^{2}} = \frac{- 1247689}{- 100 D^{2}}$

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

Cancel the common factor.

$\frac{h D^{2}}{D^{2}} = \frac{- 1247689}{- 100 D^{2}}$

Divide $h$ by $1$ .

$h = \frac{- 1247689}{- 100 D^{2}}$

Simplify the right side.

Dividing two negative values results in a positive value.

$h = \frac{1247689}{100 D^{2}}$

The final solution is all the values that make $0.01 h (1247689 - 100 h D^{2}) = 0$ true.

$h = 0$

$h = \frac{1247689}{100 D^{2}}$

$h = 0$

$h = \frac{1247689}{100 D^{2}}$

Solve for h D(h)=111.7 square root of h

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