Solve for h t = square root of (2h)/g

$t = \sqrt{\frac{2 h}{g}}$

Step 1

Rewrite the equation as $\sqrt{\frac{2 h}{g}} = t$ .

$\sqrt{\frac{2 h}{g}} = t$

Step 2

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

${\sqrt{\frac{2 h}{g}}}^{2} = t^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

${(\frac{2 h}{g})}^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{2 h}{g})}^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

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

Simplify.

$\frac{2 h}{g} = t^{2}$

Step 4

Solve for $h$ .

Multiply both sides by $g$ .

$\frac{2 h}{g} g = t^{2} g$

Simplify the left side.

Cancel the common factor of $g$ .

Cancel the common factor.

$\frac{2 h}{g} g = t^{2} g$

Rewrite the expression.

$2 h = t^{2} g$

Divide each term in $2 h = t^{2} g$ by $2$ and simplify.

Divide each term in $2 h = t^{2} g$ by $2$ .

$\frac{2 h}{2} = \frac{t^{2} g}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 h}{2} = \frac{t^{2} g}{2}$

Divide $h$ by $1$ .

$h = \frac{t^{2} g}{2}$