The square root property says the value of a variable in an equation is not changed by taking the square root of both sides of the equation. It is used to solve equations involving squares and square roots. Example x^2 + 2 = 18 x^2 = 16 (rely on the addition property. Add -2 to both sides.) ±√(x^2) = ±√16 (rely on the square root property) x = ±4
Note that the square root of a positive quantity may be either positive or negative. The third line of the example points out that this works for variables as well as numbers. That line represents four (4) cases. The two cases on the fourth line are equivalent. Here are the four cases. +x = +4 -x = +4 +x = -4 (equivalent to +x = -4) -x = -4 (equivalent to +x = +4) As a consequence, we generally jump directly from line 2 (x^2=16) to line 4 (x=±4) without the intermediate step of identifying ± cases on both sides.
Note that the square root of a positive quantity may be either positive or negative. The third line of the example points out that this works for variables as well as numbers. That line represents four (4) cases. The two cases on the fourth line are equivalent. Here are the four cases. +x = +4 -x = +4 +x = -4 (equivalent to +x = -4) -x = -4 (equivalent to +x = +4) As a consequence, we generally jump directly from line 2 (x^2=16) to line 4 (x=±4) without the intermediate step of identifying ± cases on both sides.