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Question 465069: How do you construct a segment of length sqrt 8?
Found 2 solutions by robertb, tinbar:
Answer by robertb(5830)   (Show Source):
Answer by tinbar(133)  (Show Source):
You can put this solution on YOUR website! When you say construct, do you mean it in the literal sense? As in using a piece of paper for example? Or do you mean construct in a theoretical sense, like, 'do the following steps..'
If you mean it in the literal sense, then I'll assume you have a ruler.
Get a piece of paper bigger than 8 units( I'm not sure what units you are using as you have not specified, but let's say cm for now since that's what rulers measure, generally)
Now before we figure out what lengths we should draw, let's come up with an idea to get our desired length. We want sqrt 8, and one good way to go about this is to use Pythagoreas' theorem, which says for a right angle triangle which has base a, height b, and hypotneuse c, the relationship a^2+b^2=c^2 is always true.
If we draw a base of length 1 and a height of length 1, then our hypotneuse is sqrt 2, since a=1, b=1 and c=sqrt(1^2+1^2), c = sqrt 2
Now sqrt 8 is the same as saying sqrt (4*2) since 4*2 = 8. Sqrt (4*2)= sqrt(4)*sqrt(2) since sqrt distributes over a product of numbers, now we know sqrt 4 is just 2, so ultimately we can say sqrt 8 = 2*sqrt2. We already know we need base and height of 1 cm and then the exact length of the hypotneuse is sqrt 2, but we want sqrt 8, and we know sqrt 8 is 2*sqrt(2) so all we have to do is multiply our base and height by 2 resulting in 2 cm each
So basically, take a piece of paper. Draw a horizontal line of 2 cm, then on either end of the line draw a vertical line of 2 cm, now join the missing line segment to make it a right-angle triangle. That resulting segment will be EXACTLY sqrt 8
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