1. Use "decomposing" to answer the question bellow. A. What is the area of square E?
B. What is it's side length?

2. If √17 (square root of 17) is a side length of a square, what does that mean about the area? Explain.

3. What is a rational number? Give an example.

4. What is an irrational number? Give an example.

Estimate the value of √70 (square root of 70). Show your work and explain.

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1A: 29 units²

1B: √29 units

2, 3, 4. see below

5. between 8 and 8.5

Step-by-step explanation:

1A: Split the given square up into 4 triangles and a square in the centre. You'll get 4 triangles of sides 5 and 2, and a centre square of sides 3.

Area = 4(0.5)(5 x 2) + (3²) = 29 units²

1B: Square root your answer in 1A. √29 units

Alternatively you can use Pythagoras' theorem on one of the triangles. √(5² + 2²) = √29 units

2. The area is exactly 17 units, because the area of a square is the length of its side squared. (√17)² = 17, hence the square's area is 17 units.

3. A number that can be expressed as a fraction (includes whole numbers). E.g. 1/2, 1/7, 4

4. A number that cannot be expressed as a fraction. E.g. π, e, √3

5. Consider the closest square numbers to 70. 70 is closer to 64 than 81 (difference of 6 vs 11). Hence √70 should be closer to 8 than 9. Your answer should be between 8 and 8.5.

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9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841