# How do you solve sqrt (t) - 1 + 3 = 9?

Mar 20, 2018

See a solution process below:

#### Explanation:

First, combine the constants on the left side of the equation:

$\sqrt{t} + \left(- 1 + 3\right) = 9$

$\sqrt{t} + 2 = 9$

Next, subtract $\textcolor{red}{2}$ from each side of the equation to isolate the radical while keeping the equation balanced:

$\sqrt{t} + 2 - \textcolor{red}{2} = 9 - \textcolor{red}{2}$

$\sqrt{t} + 0 = 7$

$\sqrt{t} = 7$

Now, square both sides of the equation to solve for $t$ while keeping the equation balanced:

$\left(\sqrt{t}\right) = {7}^{2}$

$t = 49$

Mar 20, 2018

$t = 49$

#### Explanation:

$\text{simplify the left side of the equation}$

$\Rightarrow \sqrt{t} + 2 = 9$

$\text{subtract 2 from both sides}$

$\sqrt{t} \cancel{+ 2} \cancel{- 2} = 9 - 2$

$\Rightarrow \sqrt{t} = 7$

$\left[\text{note that } \sqrt{a} \times \sqrt{a} = {\left(\sqrt{a}\right)}^{2} = a\right]$

$\textcolor{b l u e}{\text{square both sides}}$

${\left(\sqrt{t}\right)}^{2} = {7}^{2}$

$\Rightarrow t = 49$