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## Quadratics: Using Square Roots and Zero Property

#### High School - HSA-REI.B.4b

How to use Square Roots and Zero Property when solving Quadratic Equations? Using the square root method is one of the best methods for quadratic equation, especially when it contains the x2 terms. The general approach is to collect all the x2 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. For example,x2 - 1 = 24 Now its time to isolate the only x2 term eft n 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. x2 - 1 + 1 =24 + 1, x2 =25, x = ±5 or x = 5, x = -5 The other method is using the zero property. The zero property states that when ab = 0, then a = 0 or b = 0 or both a and b are equal to 0. For example, 5x2 + 15x = 0 Taking common factors, 5a (x + 3) = 0, X = -3. The key section of worksheets that help students be able to solve quadratics by using the square root method and the concept of zero property.

### Printable Worksheets And Lessons  #### 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.