1. Chapter 8
Section 1

2. 8.1 Evaluating Roots Find square roots.
Decide whether a given root is rational, irrational, or not a real number.
Find decimal approximations for irrational square roots.
Use the Pythagorean theorem.
Use the distance formula.
Find cube, fourth, and other roots. 2 3 4 5 6

3. Objective 1
Find square roots.
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4. Find square roots. Square Root
When squaring a number, multiply the number by itself. To find the square root of a number, find a number that when multiplied by itself, results in the given number. The number a is called a square root of the number a 2.
Square Root
A number b is a square root of a if b2 = a.
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5. Find square roots. (cont’d)
The positive or principal square root of a number is written with
the symbol
The symbol is used for the negative square root of a number.
The symbol , is called a radical sign, always represents the
positive square root (except that ). The number inside the
radical sign is called the radicand, and the entire expression—radical
sign and radicand—is called a radical.
Radical Sign
Radicand
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6. Find square roots. (cont’d)
The statement is incorrect. It says, in part, that a positive number equals a negative number.
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7. Finding All Square Roots of a Number
EXAMPLE 1
Finding All Square Roots of a Number
Find all square roots of 64.
Solution:
Slide 8.1-7

8. EXAMPLE 2 Finding Square Roots Find each square root. Solution:
Slide 8.1-8

9. Squaring Radical Expressions
EXAMPLE 3
Squaring Radical Expressions
Find the square of each radical expression.
Solution:
Slide 8.1-9

10. Objective 2
Decide whether a given root is rational, irrational, or not a real number.
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11. Deciding whether a given root is rational, irrational, or not a real number.
All numbers with square roots that are rational are called perfect squares.
Perfect Squares
Rational Square Roots 25
144
A number that is not a perfect square has a square root that is irrational. Many square roots of integers are irrational.
Not every number has a real number square root. The square of a real number can never be negative. Therefore, is not a real number.
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12. Identifying Types of Square Roots
EXAMPLE 4
Identifying Types of Square Roots
Tell whether each square root is rational, irrational, or not a real number.
Solution:
Not all irrational numbers are square roots of integers. For example  (approx ) is a irrational number that is not an square root of an integer.
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13. Find decimal approximations for irrational square roots.
Objective 3
Find decimal approximations for irrational square roots.
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14. Find decimal approximations for irrational square roots.
Even if a number is irrational, a decimal that approximates the number can be found using a calculator.
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15. Approximating Irrational Square Roots
EXAMPLE 5
Approximating Irrational Square Roots
Find a decimal approximation for each square root. Round answers to the nearest thousandth.
Solution:
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16. Use the Pythagorean theorem.
Objective 4
Use the Pythagorean theorem.
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17. Use the Pythagorean theorem.
Many applications of square roots require the use of the Pythagorean formula.
If c is the length of the hypotenuse of a right triangle, and a and b are the lengths of the two legs, then
Be careful not to make the common mistake thinking that
equals
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18. Solution: EXAMPLE 6 Using the Pythagorean Theorem
Find the length of the unknown side in each right triangle. Give any decimal approximations to the nearest thousandth.
Solution: 11 8 ?
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19. EXAMPLE 7
Using the Pythagorean Theorem to Solve an Application
A rectangle has dimensions of 5 ft by 12 ft. Find the length of its diagonal.
5 ft
12 ft
Solution:
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20. Use the distance formula.
Objective 5
Use the distance formula.
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21. Use the distance formula.
The distance between the points and is
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22. Using the Distance Formula
EXAMPLE 8
Using the Distance Formula
Find the distance between and
Solution:
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23. Find cube, fourth, and other roots.
Objective 6
Find cube, fourth, and other roots.
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24. Find cube, fourth, and other roots.
Finding the square root of a number is the inverse of squaring a number. In a similar way, there are inverses to finding the cube of a number or to finding the fourth or greater power of a number.
The nth root of a is written
In the number n is the index or order of the radical.
Radical sign
Index
Radicand
It can be helpful to complete and keep a list to refer to of third and fourth powers from 1-10.
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25. EXAMPLE 9 Finding Cube Roots Find each cube root. Solution:
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26. EXAMPLE 10
Finding Other Roots
Find each root.
Solution:
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27. HL 8.1
Book Beginning Algebra
Page 501 Exercises 43 to 50
Exercises 65,66,67