# How do you solve sqrt(4a + 1) = 1  and find any extraneous solutions?

Mar 29, 2017

Square both sides.
Solve the resulting equation.
Check the solution.

#### Explanation:

Given: $\sqrt{4 a + 1} = 1$

Square both sides:

$4 a + 1 = 1$

Subtract 1 from both sides:

$4 a = 0$

Divide both sides by 4:

$a = 0$

Check the solution:

$\sqrt{4 \left(0\right) + 1} = 1$

$1 = 1$

This checks.

There is 1 and only 1 solution and it checks, therefore, there are no extraneous solutions.