Final answer:
To solve the equation (p-5)² = 2 using the square root property, take the square root of both sides, simplifying to p - 5 = ±√2, and solve for p to get p = 5 ± √2, thus finding two possible solutions.
Step-by-step explanation:
To apply the square root property to the equation (p-5)² = 2, we first take the square root of both sides of the equation. This reads as:
√(p-5)² = √2
Which simplifies to:
p - 5 = ±√2
To find the value of p, we solve for p by adding 5 to both sides:
p = 5 ± √2
Therefore, there are two possible solutions to the original equation, p = 5 + √2 and p = 5 - √2.
This completes the square and gives us the solution set for p.