Square Root Property
Solve quadratic equations using the Square Root Property: isolate the squared term then take plus-or-minus the square root of both sides to find both solutions without factoring.
Key Concepts
If $x^2 = a$, then $x = \pm\sqrt{a}$ for any $a 0$.
Common Questions
What is the Square Root Property for quadratic equations?
The Square Root Property states that if x^2=k then x=plus-or-minus the square root of k. It applies whenever you can isolate a perfect square expression on one side. Remember to include both positive and negative roots since both are valid when k>0.
How do you apply the Square Root Property to (x-3)^2=16?
Since (x-3) is already isolated, take the square root of both sides: x-3=plus-or-minus 4. Solve each case: x-3=4 gives x=7, and x-3=-4 gives x=-1. Both solutions should be verified in the original equation.
When does the Square Root Property give no real solutions?
If the equation gives x^2=k where k<0, then the square root is not a real number and there are no real solutions. Solutions are complex: x=plus-or-minus i times the square root of |k|. When k=0 there is exactly one repeated real solution x=0.