Download Unit 6 Section 4 - American River College!

Pre Algebra
Section 6.4
Unit 6 – Coordinate Plane and Geometry
Section 4 – Pythagorean Theorem
Square Roots Revisited
In Chapter 3 Section 4 we discussed square roots – we will review a few more examples here.
Example 1)
√
√49
What number times itself is 49?
7 ∙ 7 = 49
√49 =7
Example 2)
√
√64 = √8 ∙ 8 = 8
Example 3)
What numbers does √ fall between?
Since 4 < 8 < 9,
√4 < √8 < √9
2 < √8 < 3
So √8 2 3.
American River College
337
Milano
Pre Algebra
Section 6.4
Challenge:
Simplify √.
√8
We begin by looking for the perfect square in 8.
= √4 ∙ 2
4∙2=8
= √4 ∙ √2
= 2√2
Pythagorean Theorem
In a right triangle -there is a special relationship between the sides of the triangle.
+ = Where c is the hypotenuse (the longest side) and a and b are the legs of the triangle.
Example 4)
If = ! "# $ = %& !, find c.
Note: 225 = has TWO solutions.
+ = c =15 and c= - 15
We are dealing with length so the
answer must be positive.
9 + 12 = 81 + 144 = 225 = 225 is a perfect square since 15 x15 =225 – length is
always positive.
c must be 15 , so the Hypotenuse is 15cm.
American River College
338
Milano
Pre Algebra
Section 6.4
Example 5)
If
= )*+ "# = )*+, *-"# $.
+ = 36 + = 39
1296 + = 1521
We need to subtract 1296 from both sides
= 225
Then think of the square root of 225.
Since b is the side of a triangle is must be positive - So b=15ft
American River College
339
Milano
Pre Algebra
Section 6.4
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American River College
340
Milano
Pre Algebra
Section 6.4
Exercise 6.4
NAME:___________________________________
Find the following square roots
1. √4
2. √9
3.√25
4. √144
5. √900
6. √196
What whole numbers do the following square roots fall between?
7. √7
8. √22
9.√120
For Problems 10-15, refer to the triangle below.
10. = 3/, = 4/, =?
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11. = 51, = 121, =?
341
12. = 6, = 8, =?
Milano
Pre Algebra
Section 6.4
13. = 26, = 24, =?
14. = 51, = 31, =?
15. = 15/, = 12 /, =?
16. A wheel chair ramp raises a wheel chair a vertical distance of 3 feet, in a horizontal distance of 4
feet. How long is the ramp the wheel chair travels on?
?
3
4
Challenge: break the following into simplified roots
a. √20
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b. √18
342
c.√32
Milano