# How do you solve 5+sqrt(g-3)=6 and check your solution?

Jul 6, 2017

$g = 4$

#### Explanation:

$5 + \sqrt{g - 3} = 6$

Subtract $5$ from each side.

$5 - 5 + \sqrt{g - 3} = 6 - 5$

$\sqrt{g - 3} = 1$

Square both sides.

$g - 3 = {1}^{2}$

Since the square of $1$ is $1$:

$g - 3 = 1$

Add $3$ to each side.

$g - 3 + 3 = 1 + 3$

$g = 4$

To check substitute $g$ with $4$ in the original equation:

$5 + \sqrt{g - 3} = 6$

$5 + \sqrt{4 - 3} = 6$

$5 + \sqrt{1} = 6$

The square root of $1$ is either $+ 1$ or $- 1$. Taking it to be $+ 1$:

$5 + 1 = 6$

We can use slightly different steps for the last two steps to confirm the solution:

$5 + \sqrt{1} = 6$

Subtract $5$ from each side.

$5 - 5 + \sqrt{1} = 6 - 5$

$\sqrt{1} = 1$

Square both sides. The square of $1$ is $1$.

$1 = 1$