Roots and Radicals
Section 10.1 Solving Quadratic Equations by the Square
Root Property
The Square root Property
Ex:![](./articles_imgs/6319/roots_52.gif)
Solve:
Ex: ![](./articles_imgs/6319/roots_53.gif)
Ex: ![](./articles_imgs/6319/roots_54.gif)
Ex: ![](./articles_imgs/6319/roots_55.gif)
Ex: ![](./articles_imgs/6319/roots_56.gif)
Ex: ![](./articles_imgs/6319/roots_57.gif)
Ex: ![](./articles_imgs/6319/roots_58.gif)
Ex: ![](./articles_imgs/6319/roots_59.gif)
Ex: ![](./articles_imgs/6319/roots_60.gif)
Ex: ![](./articles_imgs/6319/roots_61.gif)
Ex: ![](./articles_imgs/6319/roots_62.gif)
Ex: ![](./articles_imgs/6319/roots_63.gif)
Solve each quadratic equation by first factoring the
perfect square trinomial on
the left side. Then apply the square root property. Simplify radicals, if
possible.
EX: ![](./articles_imgs/6319/roots_64.gif)
EX: ![](./articles_imgs/6319/roots_65.gif)
Use the Pythagorean Theorem to find the missing length in
each right triangle.
Express the answer in radical form and simplify, if possible.
![](./articles_imgs/6319/roots_66.gif)
![](./articles_imgs/6319/roots_67.gif)
![](./articles_imgs/6319/roots_68.gif)
Review Exam #8
Evaluate each expression, or state that the expression is not a real number.
![](./articles_imgs/6319/roots_69.jpg)
Use a calculator to approximate each expression. Round to
three decimal places. If the expression is not a real
number so that an approximation is not possible say so.
![](./articles_imgs/6319/roots_70.gif)
Find each cube root.
![](./articles_imgs/6319/roots_71.gif)
Find the indicated root, or state that the expression is
not a real number.
![](./articles_imgs/6319/roots_72.gif)
Use the product rule for square roots to find each
product.
![](./articles_imgs/6319/roots_73.jpg)
Simplify each expression. If the expression cannot be
simplified say so.
![](./articles_imgs/6319/roots_74.jpg)
![](./articles_imgs/6319/roots_75.gif)
Multiply and, if possible, simplify.
![](./articles_imgs/6319/roots_76.jpg)
Simplify using the quotient rule for square roots.
![](./articles_imgs/6319/roots_77.jpg)
Simplify each radical expression.
![](./articles_imgs/6319/roots_78.jpg)
Solve the quadratic equation by the square root property.
If possible, simplify radicals or rationalize denominators.
![](./articles_imgs/6319/roots_79.jpg)
Solve the quadratic equation by first factoring the
perfect square trinomial on the left side. Then apply the square
root property. If possible, simplify radicals or rationalize denominators.
![](./articles_imgs/6319/roots_80.jpg)
Use the Pythagorean Theorem to find the missing length in
the right triangle. Express the answer in radical form,
and simplify if possible.
![](./articles_imgs/6319/roots_81.gif)
![](./articles_imgs/6319/roots_82.gif)
Answer Key
1. 4
2. ![](./articles_imgs/6319/roots_90.gif)
3. Not a real number.
4. 5
5. Not a real number.
6. 10.449
7. 2.646
8. -4
9. ![](./articles_imgs/6319/roots_91.gif)
10. 1
11. Not a real number.
12. 2
![](./articles_imgs/6319/roots_83.jpg)
![](./articles_imgs/6319/roots_84.jpg)
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