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Why don’t tape measures show √2?


measures1Your boss asks you to cut a length of wood exactly to √2. So, you get out your tape measure and ….what? There is NO √2! There should be though? After all, √2 is an exact length!! It was worked out on a calculator so you should be able to measure it? Why don’t rulers and tape measures show √2, just like our calculators?

The problem, you see, is that √2 is an irrational number. In other words, it never occupies an exact place on a ruler or tape measure. Irrational numbers, like √2 and pi, have infinite, non-recurring, decimal expansions. Therefore, it is only as accurate as you need it to be. For example, √2 = 1.4 which might, for example, be a distance in kms. 1.4km = 1400m. But √2 also = 1.41 which is 1410m and so on. You set the expansion of √2 to suit what you are measuring. That is why tape_measureyou don’t find √2 on your ruler! √2 is also a great reason to think about abstract ideas in Mathematics, which is a bit like an Alice in Wonderland for numbers!


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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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