Question

solve the quadratic equation by the square root method and write the solutions in radical form. simplify the solutions.
$3y^2 = 96$
answer
$y = \square$ or $\square$

Explanation:

Step1: Isolate $y^2$ term

Divide both sides by 3:
$\frac{3y^2}{3} = \frac{96}{3}$
$y^2 = 32$

Step2: Take square roots of both sides

Apply square root property:
$y = \pm\sqrt{32}$

Step3: Simplify the radical

Factor 32 into perfect square:
$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$
So $y = \pm4\sqrt{2}$

Answer:

$y = 4\sqrt{2}$ or $y = -4\sqrt{2}$