How to find square root of prime numbers?

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Calculator.

Google.  Search for sqrt(7)

If you want to compute it yourself, you can do this:

What is the square root of 7?

What is 2 squared?  4.  Smaller than 7.

What is 3 squared?  9.  Bigger than 7.

So the square root of 7 has to be between 2 and 3, something like 2.stuff

How about 2.5 squared?  6.25.  Too small, so the square root of 7 is bigger than 2.5.

How about 2.7 squared?  7.29.  Too big, so the square root of 7 is smaller than 2.7.

How about 2.6 squared?  6.76.  Too small, so the square root of 7 is bigger than 2.6.  The square root of 7 is 2.6something

You can keep following this process (we found that the square root of 7 is 2.something, then 2.6something, and so on) to get closer and closer to the square root of 7, but square roots of prime numbers (accept 1) are irrational, which means their decimal value never ends.

You can keep going and find that the square root of 7 is 2.64755131106, or even like Robert Nemiroff at NASA did in calculating the square root of 7 to one million places past the decimal (here http://apod.nasa.gov/htmltest/gifcity/sqrt7.1mil ), but you'll never get to the end because there is no end.

by Level 13 User (103k points)

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