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Some square roots can easily be calculated by hand. For example the square root of 4 is 2 and of 9 is 3. However, most of them are irrational which means that cannot be put in the form p/q where p and q are integers and q is not zero. So how do we find real numbers by hand that are irrational?

The best we can do is to approximate them. There are many ways to do this.

I will give you a link to a Wikipedia article that lists these:

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Q: Calculate square root by hand
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