Questions: Solve the equation by using the square root property. (3p+1)^2=12 The solution set is

Transcript text: Solve the equation by using the square root property. \[ (3 p+1)^{2}=12 \] The solution set is $\square$

Solution

Solution Steps

To solve the equation $(3p + 1)^2 = 12$ using the square root property, follow these steps:

Take the square root of both sides of the equation.
Solve for $p$ by isolating it on one side of the equation.

Step 1: Apply the Square Root Property

Given the equation: \[ (3p + 1)^2 = 12 \] Take the square root of both sides: \[ 3p + 1 = \pm \sqrt{12} \]

Step 2: Simplify the Square Root

Simplify $\sqrt{12}$: \[ \sqrt{12} = 2\sqrt{3} \] Thus, the equation becomes: \[ 3p + 1 = \pm 2\sqrt{3} \]

Step 3: Solve for $p$

Solve for $p$ by isolating it on one side: \[ 3p + 1 = 2\sqrt{3} \quad \text{or} \quad 3p + 1 = -2\sqrt{3} \] For the first equation: \[ 3p = 2\sqrt{3} - 1 \] \[ p = \frac{2\sqrt{3} - 1}{3} \] For the second equation: \[ 3p = -2\sqrt{3} - 1 \] \[ p = \frac{-2\sqrt{3} - 1}{3} \]