Given a segment of length, show two different ways for constructing a segment of length (i) (square root of (a19)) *and (ii)a* (square root of (a2/3))

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- Oct 29th 2010, 08:23 PMMATNTRNGConstructing a Segment
Given a segment of length

, show two different ways for constructing a segment of length (i) (square root of (**a****19**)) *and (ii)**a*** (square root of (**a****2/3**)) - Oct 29th 2010, 11:40 PMOpalg
Start by assembling a checklist of techniques for constructing segments whose length is some multiple of $\displaystyle a$. For example, can you construct one with length $\displaystyle ka$ (where $\displaystyle k$ is a whole number)? What about $\displaystyle a/k$? ... or $\displaystyle \sqrt2a$? What about $\displaystyle \sqrt ka$ for other values of $\displaystyle k$? (Think of a right-angled triangle in which two sides are known multiples of $\displaystyle a$. What will be the length of the hypotenuse?)