Solve for h 100=( square root of h)/4

$100 = \frac{\sqrt{h}}{4}$

Step 1

Rewrite the equation as $\frac{\sqrt{h}}{4} = 100$ .

$\frac{\sqrt{h}}{4} = 100$

Step 2

Multiply both sides of the equation by $4$ .

$4 \frac{\sqrt{h}}{4} = 4 \cdot 100$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{\sqrt{h}}{4} = 4 \cdot 100$

Rewrite the expression.

$\sqrt{h} = 4 \cdot 100$

Simplify the right side.

Multiply $4$ by $100$ .

$\sqrt{h} = 400$

Step 4

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

${\sqrt{h}}^{2} = 400^{2}$

Step 5

Simplify each side of the equation.

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

${(h^{\frac{1}{2}})}^{2} = 400^{2}$

Simplify the left side.

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

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

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

$h^{\frac{1}{2} \cdot 2} = 400^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$h^{\frac{1}{2} \cdot 2} = 400^{2}$

Rewrite the expression.

$h^{1} = 400^{2}$

Simplify.

$h = 400^{2}$

Simplify the right side.

Raise $400$ to the power of $2$ .

$h = 160000$