Solve for d t = square root of d/16

$t = \sqrt{\frac{d}{16}}$

Step 1

Rewrite the equation as $\sqrt{\frac{d}{16}} = t$ .

$\sqrt{\frac{d}{16}} = t$

Step 2

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

${\sqrt{\frac{d}{16}}}^{2} = t^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{d}{16}}$ as ${(\frac{d}{16})}^{\frac{1}{2}}$ .

${({(\frac{d}{16})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

Simplify ${({(\frac{d}{16})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{d}{16})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{d}{16})}^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{d}{16})}^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

${(\frac{d}{16})}^{1} = t^{2}$

Simplify.

$\frac{d}{16} = t^{2}$

Step 4

Solve for $d$ .

Multiply both sides of the equation by $16$ .

$16 \frac{d}{16} = 16 t^{2}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$16 \frac{d}{16} = 16 t^{2}$

Rewrite the expression.

$d = 16 t^{2}$