solve each equation by taking the square roots

Question

p^2 + 5 = 24

Answer 1

To solve the equation \( p^2 + 5 = 24 \) by taking square roots, follow these steps:

1. Subtract 5 from both sides of the equation: \[ p^2 + 5 - 5 = 24 - 5 \] This simplifies to: \[ p^2 = 19 \]

2. Now, take the square root of both sides. Remember to consider both the positive and negative square roots: \[ p = \pm \sqrt{19} \]

Thus, the solutions are: \[ p = \sqrt{19} \quad \text{and} \quad p = -\sqrt{19} \]