# Quadratics: Square Roots and Zero Property Worksheets

You would be surprised how often quadratic equations are used to model every day ordinary things like the speed of airplanes and various business analytics that help business owners understand the health of their businesses. Like any model, in order to make sense of it, we have to manipulate variables within it. When that is needed, we will often need to be able to determine the solution to these quadratics. We have covered other methods to solve quadratics, but now we focus on the use of square roots and the zero product property to achieve this. The key section of worksheets that help students be able to solve quadratics by using the square root method and the concept of zero product property.

### Aligned Standard: HSA-REI.B.4b

- Zero Property Step-by-step Lesson- We rework the Zero Product Property to kick this unit off.
- Guided Lesson - We introduce squares and roots in this one.
- Guided Lesson Explanation - I try to break these down in different ways. There are numerous directions you can take to solve these problems.
- Practice Worksheet - All the problems that involving squares, start as squares.
- Matching Worksheet - Find the matching possible values of each variable.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

The Zero Property is found on page 1 and 3. Page 2 is dedicated to square roots.

- Homework 1 - Solve for m and write your answers as integers or as proper or improper fractions in simplest form.
- Homework 2 - Solve and write your answers as integers or as proper or improper fractions in simplest form.
- Homework 3 - Jam it all together to get this zero into a hero.

### Practice Worksheets

Practice pages 1 and 2 focus on the zero property. Square roots finish off this section for us.

- Practice 1 - We know that the Zero Product Property states that for all real numbers a and b: If ab = 0, then a = 0 or b = 0
- Practice 2 - Solve for d and write your answers as integers, decimals or proper or improper fractions in the simplest form.
- Practice 3 - Just take the square root of the other side and you are good to go.

### Math Skill Quizzes

The first one is just on the zero property. The last two mix the use of both skills.

- Quiz 1 - Find the value of g: (g – 112) (g – 425) = 0
- Quiz 2 - Find the value of w: (w –500) (w – 242) = 0
- Quiz 3 - A mixture of many different problem types for you.

### How Do You use the Square Root Property to Solve Quadratic Equations?

Using the square root method is one of the best methods for quadratic equation, especially when it contains the x^{2} terms. The general approach is to collect all the x^{2} and to put them on one side and to put the constants on the other. Once you have done that, take the square roots on both sides and finding out the value of x. It is important that you attach ± when you get the square root of the constant. Since that would cover both possible values.

For example, x^{2} - 1 = 24. Now it is time to isolate the only x^{2} term on the left side through adding +1 on both sides. Then you solve the equation for the square root on both sides of the equation. As mentioned earlier, it is important that you attach the minus or plus symbol to the constant’s square root.

x^{2} - 1 + 1 = 24 + 1, x^{2} =25, x = ±5 or x = 5, x = -5

### What is the Zero Product Property?

This property simply states that if you multiply a series of expressions and the result is zero, at least one of those expression must be zero. Which makes sense when you think about it, if you multiply a bunch of things together and you end up with a final product of zero, something must have been zero within it. In math form, we state this as: if a × b × c = 0, then a = 0, or b = 0, or c = 0.

You can use this property to solve possible values of variables within an equation. You will find using this strategy will result in multiple possible answers. You can use this to solve linear equations such as: x^{2} - 5x + 6.

**Step 1) Factor** - x^{2} - 5x + 6

a) ( x^{2} - 2x) + (-3x + 6) : Split the expression up into groups.

b1) left side: x(x - 2): factor out x.

b2) right side: -3(x - 2): factor out -3.

b3) We are left with: x(x - 2) -3(x - 2)

c) (x-2)(x-3) : factor out (x-2).

**Step 2) Apply zero product property to factors** x - 2 = 0 or x – 3 = 0. This would tell us that x is either 2 or 3.