Using the Pythagorean Relationship

Key Ideas Review.
Okay,so I'm doing odds,and I think Karen is doing evens.
Pg.30-31

1.The Pythagorean relationship can be used to determine the length of the hypotenuse of a right triangle when the lengths of the two legs are known. AGREE?

3.Determine the length of the hypotenuse.Show your work.
a)


k² + j² = l²
40cm² + 9cm² = l²
(40² x 40²) + (9² x 9²) = l²
1600cm² + 81cm² = 1681cm²
√1681cm² = √l²
41cm²


b)
p² + q² = r² 12m² + 35m² = r² (12² x 12² ) + (35² + 35²) = r²
144m² + 1225m² = 1369m²
√1369m² = √r²
37cm²




5.Calculate the missing side length for each right triangle,to the nearest tenth of a centimeter.Show your work.
a)


w² + x² = y²
w² + 25² = 36²
11 = 25 - 36
√11 = 3.3
3.3²




b)


f² + g² = h²
7cm² + g² = 12cm²
49cm² + g² = 144cm²
144cm² - 49cm² = 95cm²
√95cm² = 9.7cm²
9.7cm²



7.A triangle is made up of two smaller congruent right triangles.








a)Find the Length of the hypotenuse for the right triangle,to the nearest tenth of a metre.Show your work.

4m² + 2m² = b²
(4 x 4) + (2 x 2) = b²
16m² + 4m² = b²
√20m² = 4.5m
b = 4.5m


b)Calculate the perimeter of the large triangle,to the nearest tenth of a metre.Show your work.
I don't know how to do this one..Help?

Filimon Scribe Post

Home work: 98-100

9 pg 99- 17-18-19-20-21-2-23-24

15 pg 100- Arrange these number to least to greatest square- root of 27 - square root of 46- 5.8- 6.3- 7

If anyone can tell me how to make the square root sign please tell me in the comment box

below. Thanks!

Ishaka's square roots scribe post

4) Estimate the square root of each number, to one decimal place. Check with a calculator.

a) 72
square root 64 =8 x 8
square root 72 = 8.__x 8.__
square root 81 = 9 x 9

I estimated that 8.49 was the square root of 72 calculator 8.48

b) 103
square root 100 = 10 x 10
square root 103 = 10.__ x 10.__
square root 121 = 11 x 11

I estimated that 10.15 x 10.15 was the square root of 103 calculator 10.14

c) 55
square root 49 = 7 x 7
square root 55 = 7.__ x 7.__
square root 64 = 8 x 8

I estimated that 7.42 x 7.42 was the square root of 55 calculator 7.41




6) What is an example of a whole number that has a square root between 9 and 10?

9 10
81 100

examples: 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.

Victoria's Square Root Post

Stella is planning an outdoor wedding. She would like a square dance floor with an area of 115 m2.

a) Determine the side length of the dance floor, to the nearest tenth of a metre.

b) Stella finds out that the dance floor will be made up of floorboards that each measure 1 m2. What are the two side lengths the dance floor can have that are closest to what she wants?

c) What are the two square areas for the dance floor that Stella can choose from?

d) Which area will Stella choose? Explain.

Answers !

a.)10.7m b.) Sorry i dont know this question c.)100m2 or 121m2 d.) She will chose the 121m2 dance floor because its closer to the size she wanted.

New Question !

14. Alex is thinking of a number.

a) What number could he be thinking of?

b) Is there more than one answer? Explain

Answers!

a.) 60 b.) No, there is only one answer and the nember must be between 49 and 64. The only multiple number is 12m this is the range of 60.

Richards Scribe Post

Pages 98-100

16.a) 27m squared b) i cant find the answer . can you try finding the answer by commenting.

17.a) 324cm squared b)1296cm squared c) 36cm by 36cm squared

Kevin's Square Root Scribe Post

Show you know:
a) Identify a whole number with a square root between 8 and 9.
b) How many whole numbers can you find that have a square root between 8 and 9? show you work.


a) First I changed the number 8 to 64 (8x8) and 9 to 81 (9x9).

64 ? 81

64 73 81



b) There are 16 whole numbers I found.

65 = 8.0

66 = 8.12

67 = 8.18

68 = 8.24

69 = 8.30

70 = 8.36

71 = 8.42

72 = 8.48

73 = 8.54

74 = 8.60

75 = 8.66

76 = 8.71

77 = 8.77

78 = 8.83

79 = 8.88

80 = 8.94


I used perfect squares to find these.


P.s I'm not sure if I'm right so can you guys help me out? Just post your answers at the comment section and I'll take a look at them.

Justin's Square Root Scribe Post

Show you know:
For each number of the following, use perfect squares to estimate the square root to one decimal place.Check your answers with a calculator

a) ✔18 b) ✔23 c) ✔35


You can estimate using perfect squares to find the square root to one decimal place like this:

✔18 is in between the perfect numbers 16 and 25. ✔16=4x4 ✔18=4.__ ✔25=5x5
✔18=4.__ because if you multiply 4.__ it equals 18.

✔23 is in between the perfect numbers 16 and 25. ✔16=4x4 ✔23=4.__ ✔25=5x5
23=4.__ because if you multiply 4.__ it equals 23.

✔35 is in between the perfect numbers 25 and 36. ✔25=5x5 ✔35=5.__ ✔36=6x6
35=5.__ because if you multiply 5.__ it equals 35.

Karen's Scribe Post

Prime Factorization is also a way

to find out if a square is perfect or not.

Square root is the inverse (opposite) of squaring, for example:

5² = 5x5 or 25
√25 is 5 times itself has a product of 25
5x5=21 || √25=5

Yesterday's Homework

Estimating in Fractions

√1: 1

√2: 1 1/3

√3: 1 2/3

√4: 1 3/3 = 2

√5: 2 1/5

√6: 2 2/5

√7: 2 3/5

√8: 2 4/5

√9: 2 5/5 = 3

√10: 3 1/7 ...

See any patterns? The denominator is how many spaces are in between the 2 closest perfect squares. The numerator is how many spaces the square root number took going to the left.

√39 6 3/13;6.24 x 6.24

√200 14 4/29; 14.14 x 14.14

√850 841 10/59; 29.15 x 29.15

Today's Homework

(This part gets confusing but I'll try to explain it as good as I can)

- make another number line with √1 to √25 square root numbers with one and a half (1 1/2) intervals

- write the fraction x fraction = 1-25

- on the bottom, write the decimal that is almost equal to 1, 2, 3, ... 25

- lastly highlight or box the perfect square numbers

* Don't forget to use ' ' the almost equal symbol.

Jocelle Garcia's scribe post

Tell me everything you know.

1 , 1 x 1 = 1 , perfect square

2 , 1.41 x 1.41 = 2 , not a perfect square

3 , 1.73 x 1.73 = 3, not a prefect square

4 , 2 x 2 = 4, perfect square

5 , 2.23 x 2.23 = 5, not a perfect square

6 , 2.44 x 2.44 = 6 , not a perfect square

7 , 2.64 x 2.64 = 7 , not a perfect square

8 , 2.82 x 2.82 = 8 , not a perfect square

9 , 3 x 3 = 9 , perfect square

√ Square root is the inverse of squaring

5² = 5 x 5 or 25

√25 is WHAT times it self ?

has a product of 25

5 x 5 = 25 || √25 = 5

*Opposites *

+ addition , - subtraction

x multipication , ÷ division

x² squared , √ square root

NOTES :

• Use fractions to show the estimated √ ( square root ) between 1-23
• How can you use " perfect squares " to estimate √ 's ?

√39 √850 √200