+118667 Let's consider square root of 2
$${\sqrt{{\mathtt{2}}}} = {\mathtt{1.414\: \!213\: \!562\: \!373\: \!095}}$$
so how do I change 1.4142135623730951 back to square root 2. I think that is your question.
WELL that number is not square root 2 it is an approximation of it. I would need all the digits to be able to go backwards!
Mmm. This creates a problem. You see square root 2 is an irrational number which means it can not be expressed exactly as a fraction (p/q) This means it cannot be expressed as a terminating or recurring decimal either. So we cannot know all the digits.
Hence it would be impossible for an approximation to be expressed as a surd. There would always be some number (a rational one) that would be exact.
Does that make sense?
+118667 Let's consider square root of 2
$${\sqrt{{\mathtt{2}}}} = {\mathtt{1.414\: \!213\: \!562\: \!373\: \!095}}$$
so how do I change 1.4142135623730951 back to square root 2. I think that is your question.
WELL that number is not square root 2 it is an approximation of it. I would need all the digits to be able to go backwards!
Mmm. This creates a problem. You see square root 2 is an irrational number which means it can not be expressed exactly as a fraction (p/q) This means it cannot be expressed as a terminating or recurring decimal either. So we cannot know all the digits.
Hence it would be impossible for an approximation to be expressed as a surd. There would always be some number (a rational one) that would be exact.
Does that make sense?
