we have been asked to prove that it is possible to determine the value of a surd using either similar figures or Pythagoreans theorem.

Question

we have been shown how to construct the surd using a compass and ruler. but we now have to prove that our method is correct.

we know that (root)x=(root) a
* (root) b

thanks for any help.

Answer 1

I am somewhat confused.

The question on the determination is how accurate. What is the square root of 7? To how many decimal places. Your construction probably involved measuring. So how accurate is the measuring?
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If one takes any prime number, take the square root. It is an irrational number, it cannot be written down in deterministic digits.