Square root property

Definition

The square root property is a method used to solve quadratic equations by taking the square root of both sides of the equation. It is particularly useful for equations in the form $ax^2 = c$.

5 Must Know Facts For Your Next Test

1. The square root property can only be applied if the quadratic equation can be rearranged into the form $ax^2 = c$.
2. When applying the square root property, remember to consider both positive and negative roots, giving two potential solutions: $x = \pm\sqrt{c/a}$.
3. If $c$ is negative and $a$ is positive, there are no real solutions because you cannot take the square root of a negative number in real numbers.
4. The square root property simplifies solving quadratics when completing the square or factoring is cumbersome.
5. Always simplify the radical expressions if possible when using this method.

Review Questions

• How do you apply the square root property to solve $4x^2 = 16$?
• What must you remember about roots when using the square root property?
• Why can't you use the square root property directly on all quadratic equations?

Related terms

Quadratic Equation:

A polynomial equation of degree two, typically in the form $ax^2 + bx + c = 0$.

Completing the Square:

A method used to solve quadratic equations by transforming them into a perfect square trinomial.

Discriminant:

In a quadratic equation $ax^2 + bx + c = 0$, it is given by $b^2 - 4ac$ and determines the nature of roots.