Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. π , √5 ,√8 ,2√5 (a)Without using your calculator, approximate the…

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asked Jul 22, 2019 147k views

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Szymon Roziewski · Answer 1 · 2019-07-27T09:35:31+0000

(a) To approximate
$\pi$ , we are going to use a compass to draw a cirle of radius 2 and circumference 12.5. Remember that
$\pi$ is the ratio between the circumference of a circle and its diameter; since the diameter of a circle is two times its radius, we can find
$\pi$ using the equation:
$\pi = (cricunference)/(2*radius)$

$\pi = (12.5)/(2(2))$

$\pi = (12.5)/(4)$

$\pi =3.125$
And to the nearest tenth:

$\pi =3.1$

To approximate
√(2)

, we are going to use the Babylonian method:
Step 1. We are going to make a guess. Our guess is 2 because
√(4) =2

, so

must be close to 2.
Step 2. We are going to divide 5 by 2:

(5)/(2) =2.5

Step 3. We are going to find the average between our initial guest and the result of our previous calculation:

(2+2.5)/(2) = (4.5)/(2) =2.25

And to the nearest tenth:
√(5) =2.2

To approximate
√(8)

, we are going to use the Babylonian method one more time:
Step 1. Our guess is 3 because
√(9) =3

, so

must be close to 3.
Step 2. We are going to divide 8 by 3:

(8)/(3) =2.6

Step 3. We are going to find the average between our initial guest and the result of our previous calculation:

(3+2.6)/(2) = (5.6)/(2) =2.8

To approximate
2 √(5)

we are going to multiply our approximation of
√(5)

and multiply it by 2:

2 √(5) =2*2.2

(b) Since we have our irrational numbers expressed as decimal approximations, we can compare them to arrange them form least to greatest:
2.2,2.8,3.1,4.4
Now, we just need to replace the decimal approximations with the original numbers:

√(5)