unit 1 - section 1.2 web.notebook - sandra...
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Unit 1 Section 1.2 Web.notebook
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October 09, 2013
Unit 1 Section 1.2
What are the first five perfect square whole numbers?
1, 4, 9, 16, 25
What are the square roots of these numbers?
1, 2, 3, 4, 5
Which numbers are between these perfect squares?
2, 3, 5, 6, 7, 8...
What do you think their square roots will be?
Fractions and decimals between the square roots of the perfect squares
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Page 14
A ladder is leaning against a wall. For safety, the distance from the base of a ladder to the wall must be about 1/4 of the height up the wall.
What is the safe height up the wall for the ladder?
8m
How do you know?
The distance from the base of the ladder to the wall is 2m. This should be about 1/4 of the height, so the height should be
4 x 2m = 8m
How could you calculate the height of the ladder up the wall?
Pythagorean Theorem
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Square Roots
Squares
NonPerfect Squares when a number can not be written as a product of two equal fractions.
Two methods for estimating a square root of a decimal
1. Benchmarks...
• visualize a number line and the closest perfect square on each side of the number ie: 7.5 falls between 4 and 9• You choose the perfect square that the number is closest to ie: 7.5 is closer to 9, ∴√7.5 is closer to 3 than 2• An approximation for √7.5 is 2.7 or 2.8
1 4 9 16 25 36 49 64 81
1 2 3 4 5 6 7 8 9
Try these...
Unit 1 Section 1.2 Web.notebook
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2. Using a calculator
If the decimal does not appear to terminate or repeat, the square root is an approximation.
ie:
Unit 1 Section 1.2 Web.notebook
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Estimate Square Root of a Decimal...
** Closer to so closer to 8
∴ 8.2 - check on calculator
Example 1
Example 2** Closer to √16 so closer to 4, but does not exceed 4.
∴
Try these...
i)
ii)
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Estimating Square Root of a Fraction
Find the closest perfect square to the numerator and denominator
3 is closest to 4
10 is closestto 9
Example:
Try these...
i)
ii)
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Combination of two methods
There are remote cases when the fraction method does not work. When that happens we can combine the fraction and decimal strategy together...
ie: if we use the fraction strategy (method) we will end up with...
if we use a calculator we will get...
2.9 this is too big a difference, so the fraction strategy does not work; this is not a good estimate
if we change to a decimal, we can find a good estimate.
Unit 1 Section 1.2 Web.notebook
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Finding a number with a Square Root between two given numbers...
ex: Identify a decimal that has a square root between 5 & 6
Use a number line
1 4 9 16 25 36 49 64 81
1 2 3 4 5 6 7 8 9
52 = 25, so 5 is the square root of 25
62 = 36, so 6 is the square root of 36
so any decimal between 25 and 36 has a square root between 5 and 6.
Try these...
i) ID a decimal who has a square root between 7 and 8
ii) ID a decimal who has a square root between 11 and 12
Unit 1 Section 1.2 Web.notebook
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Applying the Pythagorean Theorem
You can use the Pythagorean Theorem to find unknown lengths in right triangles.
a
b
Legs
c - hypotenuse
Theorem: a2 + b2 = c2
To find the hypotenuse "c"use.... a2 + b2 = c2
To find one of the sides (legs) "a" or "b" use....
c2 - a2 = b2 or c2 - b2 = a2
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Example 1:
5
12
c
Find c
Example 2:15.8 7.4
b
Find b
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Example:
The sloping face of this ramp is to be covered in carpet.
a) Estimate the length of the ramp to the nearest tenth of a meter.
carpetlength
estimate answer
Closer to 7 ∴ 6.7
Unit 1 Section 1.2 Web.notebook
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b) Use calculator to check
c) Calculate the area of carpet needed
A= l x w = 6.7 x 2.2 = 14.74 m2 ∴ approximately 15m2 will be needed
Book Work... Pages 1819 #'s 4 22
Extra Practice 2
MidUnit Review page 21