Solving the Equation (x7)^2 = 60
This article will guide you through solving the equation (x7)^2 = 60 by using the square root property.
Understanding the Square Root Property
The square root property states that if a² = b, then a = ±√b. This property allows us to isolate the variable by taking the square root of both sides of the equation.
Solving the Equation

Take the square root of both sides: Applying the square root property, we get: √[(x7)²] = ±√60

Simplify the square roots: The square root of (x7)² is simply (x7), and we can simplify √60 as √(4*15) = 2√15. Therefore, we have: x  7 = ±2√15

Isolate x: Add 7 to both sides of the equation: x = 7 ± 2√15

The Solutions: This gives us two solutions:
 x = 7 + 2√15
 x = 7  2√15
Conclusion
By applying the square root property and simplifying the equation, we have successfully solved for x in the equation (x7)² = 60. The solutions are x = 7 + 2√15 and x = 7  2√15.