Question

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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Answer 1

1A: 29 units²

1B: √29 units

2, 3, 4. see below

5. between 8 and 8.5

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.