Solve for d t = square root of (2d)/a

$t = \sqrt{\frac{2 d}{a}}$

Rewrite the equation as $\sqrt{\frac{2 d}{a}} = t$ .

$\sqrt{\frac{2 d}{a}} = t$

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

${\sqrt{\frac{2 d}{a}}}^{2} = t^{2}$

Simplify each side of the equation.

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

${({(\frac{2 d}{a})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

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

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

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

${(\frac{2 d}{a})}^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{2 d}{a})}^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

${(\frac{2 d}{a})}^{1} = t^{2}$

Simplify.

$\frac{2 d}{a} = t^{2}$

Solve for $d$ .

Multiply both sides by $a$ .

$\frac{2 d}{a} a = t^{2} a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{2 d}{a} a = t^{2} a$

Rewrite the expression.

$2 d = t^{2} a$

Divide each term in $2 d = t^{2} a$ by $2$ and simplify.

Divide each term in $2 d = t^{2} a$ by $2$ .

$\frac{2 d}{2} = \frac{t^{2} a}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{t^{2} a}{2}$

Divide $d$ by $1$ .

$d = \frac{t^{2} a}{2}$