The problem is to solve the equation $(4x+1)^2 = 3$ using the square root property.

1. Problem Description

The problem is to solve the equation $(4x+1)^2 = 3$ using the square root property.

2. Solution Steps

We are given the equation $(4x+1)^2 = 3$. To solve for $x$, we can use the square root property.

Taking the square root of both sides gives:

$\sqrt{(4x+1)^2} = \pm \sqrt{3}$

$4x+1 = \pm \sqrt{3}$

Now we can isolate $x$ by first subtracting 1 from both sides:

$4x = -1 \pm \sqrt{3}$

Then we divide by 4:

$x = \frac{-1 \pm \sqrt{3}}{4}$

So the two solutions are $x = \frac{-1 + \sqrt{3}}{4}$ and $x = \frac{-1 - \sqrt{3}}{4}$.

3. Final Answer

The solutions are $\frac{-1 + \sqrt{3}}{4}, \frac{-1 - \sqrt{3}}{4}$.