# How do you solve for t in r = sqrt(s/t) ?

Feb 12, 2017

See the entire solution process below:

#### Explanation:

First, square each side of the equation to eliminate the radical while keeping the equation balanced:

${\left(r\right)}^{2} = {\left(\sqrt{\frac{s}{t}}\right)}^{2}$

${r}^{2} = \frac{s}{t}$

Now, multiply each side of the equation by $\frac{\textcolor{red}{t}}{\textcolor{b l u e}{{r}^{2}}}$ to solve for $t$:

$\frac{\textcolor{red}{t}}{\textcolor{b l u e}{{r}^{2}}} \times {r}^{2} = \frac{\textcolor{red}{t}}{\textcolor{b l u e}{{r}^{2}}} \times \frac{s}{t}$

$\frac{\textcolor{red}{t}}{\cancel{\textcolor{b l u e}{{r}^{2}}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{{r}^{2}}}} = \frac{\cancel{\textcolor{red}{t}}}{\textcolor{b l u e}{{r}^{2}}} \times \frac{s}{\textcolor{red}{\cancel{\textcolor{b l a c k}{t}}}}$

$t = \frac{s}{r} ^ 2$