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Unit 1 Section 1.2 Web.notebook 1 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 1: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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

Page 2: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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

Page 3: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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...

Page 4: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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:

Page 5: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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)

Page 6: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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)

Page 7: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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.

Page 8: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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

Page 9: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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

Page 10: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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Example 1:

5

12

c

Find c

Example 2:15.8 7.4

b

Find b

Page 11: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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

Page 12: Unit 1 - Section 1.2 Web.notebook - Sandra McCormacksmccormack.weebly.com/uploads/2/4/3/0/24303506/section_1... · 2018. 9. 9. · Unit 1 Section 1.2 Web.notebook 3 October 09, 2013

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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