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A =
B
SECTION 8-1 Jim Smith JCHS
3108.4.42
3108.4.14
36
81
144
9
= 6
= 9
= 12
= 3
Never Leave A Perfect Square
Under A Radical Sign
3 x 2 x 5 x 7 =
When Multiplying Or Dividing
Remember:
Whole Numbers ( Rational Numbers )
With Whole Numbers
And Radicals With Radicals.
3 5 x 2 7 =
6 35
5 5
10 15
Whole Numbers ( Rational Numbers )
With Whole Numbers
And Radicals With Radicals.
2 3
5
1
5
1
5 5
1
=
= 2 10
Never Leave A Number Under A
Radical Sign That Has A
Perfect Square As A Factor.
ab = a x b
= 5 2
40 = 4 10
x
50 25 2
= x
Never Leave A Radical In The
Denominator Of A Fraction
To Simplify This Expression We Rationalize
The Denominator. Multiply The Denominator
By Something That Gives Us A Rational
Answer. We Can Usually Multiply It By It’s
Self. Multiply The Top By The Same Thing.
3
5
=
3 5
5
5
5
x
x
2 5
3
x
x
3
3
=
=
2 15
3
=
=
5 6
2 7
x
x
7
7
5 42
2x7
=
=
5 42
14
The Geometric Mean Between
2 Numbers ( A and B ), Is The
Number That When Substituted
For X Will Make This Proportion
True
A
X
= X
B
Find the geometric mean
between 4 and 9
4
X
= X
9
X² = 36
X² = 36
X = 6
Find the geometric mean
between 3 and 15
3
X
=
X
15
X² = 45
X² = 45
X = 3 5
X = 6.7
8 is the geometric mean between
2 and what number
2
8
= 8
X
2X = 64
X = 32
A
B
The Altitude Drawn To The
Hypotenuse In A Right Triangle
Divides The Hypotenuse Into 2
Parts. The Altitude Is The Geometric
Mean Between The 2 Parts.
A
Alt
= Alt
B
8
5
X
8
X
= X
5
X² = 40
X = 40
X = 2 10
X = 6.3
Find X
Each Leg Is The Geometric
Mean Between The Part Of The
Hypotenuse Adjacent To The Leg And
The Whole Hypotenuse
Y
Z
W
X
Y
W
=
W
Y+Z
Z
X
X
Y+Z
=
8
5
R
T
8
T
= T
8+5
T² = 8 ( 13 )
T² = 104
T = 104
T = 2 26
T = 10.2
Find T
8
5
R
T
5
R
= R
5+8
R² = 5 ( 5+8 )
R² = 5 (13 )
R² = 65
R = 65
R = 8.1
Find R

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8-1 Geometric Mean.ppt

  • 1. A = B SECTION 8-1 Jim Smith JCHS 3108.4.42 3108.4.14
  • 2. 36 81 144 9 = 6 = 9 = 12 = 3 Never Leave A Perfect Square Under A Radical Sign
  • 3. 3 x 2 x 5 x 7 = When Multiplying Or Dividing Remember: Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 3 5 x 2 7 = 6 35
  • 4. 5 5 10 15 Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 2 3 5 1 5 1 5 5 1 =
  • 5. = 2 10 Never Leave A Number Under A Radical Sign That Has A Perfect Square As A Factor. ab = a x b = 5 2 40 = 4 10 x 50 25 2 = x
  • 6. Never Leave A Radical In The Denominator Of A Fraction To Simplify This Expression We Rationalize The Denominator. Multiply The Denominator By Something That Gives Us A Rational Answer. We Can Usually Multiply It By It’s Self. Multiply The Top By The Same Thing. 3 5 = 3 5 5 5 5 x x
  • 7. 2 5 3 x x 3 3 = = 2 15 3 = = 5 6 2 7 x x 7 7 5 42 2x7 = = 5 42 14
  • 8. The Geometric Mean Between 2 Numbers ( A and B ), Is The Number That When Substituted For X Will Make This Proportion True A X = X B
  • 9. Find the geometric mean between 4 and 9 4 X = X 9 X² = 36 X² = 36 X = 6
  • 10. Find the geometric mean between 3 and 15 3 X = X 15 X² = 45 X² = 45 X = 3 5 X = 6.7
  • 11. 8 is the geometric mean between 2 and what number 2 8 = 8 X 2X = 64 X = 32
  • 12. A B The Altitude Drawn To The Hypotenuse In A Right Triangle Divides The Hypotenuse Into 2 Parts. The Altitude Is The Geometric Mean Between The 2 Parts. A Alt = Alt B
  • 13. 8 5 X 8 X = X 5 X² = 40 X = 40 X = 2 10 X = 6.3 Find X
  • 14. Each Leg Is The Geometric Mean Between The Part Of The Hypotenuse Adjacent To The Leg And The Whole Hypotenuse Y Z W X Y W = W Y+Z Z X X Y+Z =
  • 15. 8 5 R T 8 T = T 8+5 T² = 8 ( 13 ) T² = 104 T = 104 T = 2 26 T = 10.2 Find T
  • 16. 8 5 R T 5 R = R 5+8 R² = 5 ( 5+8 ) R² = 5 (13 ) R² = 65 R = 65 R = 8.1 Find R