Given the equation (m + 6)² = 35, we need to find the value of m using the square root property.
The square root property is applied on quadratic equations of the form x² = c. It states that if x² = c, then x = sqrt(c) or x = -sqrt(c).
Applying the square root property to the given problem, we'll have:
m + 6 = sqrt(35) or
m + 6 = -sqrt(35)
These two equations can be solved to find the solutions for m.
For the first equation, we will subtract 6 from both sides to solve for "m".
m + 6 - 6 = sqrt(35) - 6
so, m = -6 + sqrt(35)
For the second equation, we will again subtract 6 from both sides to solve for "m".
m + 6 - 6 = -sqrt(35) - 6
so, m = -6 - sqrt(35)
Then, the solutions for the equation (m + 6)² = 35 are m = -6 + sqrt(35) and m = -6 - sqrt(35).
Hence, the solutions for the given equation are m = -6 + sqrt(35), and m = -6 - sqrt(35).