How do can you find the distance between square root 2 and -3 ?

Hi there! Thank you for the opportunity to help you with your question!

The distance between square root of 2 and -3 is the irrational number, given by their difference:

The question above is not clear, but if you want to find it numerically, you could be to create a polynomial which has this solution, say

If you set the polynomial above equal to zero, you will see that sqrt(2) + 3 [the number we're interested] is a solution.

And now, we can use a numerical method like Newton's method to find it numerically. Newton's method is given by:

If we take x_0 to be equal to 5: then we would have:

x0 = 5

x1 = 4.7143

x2 = 4.5683

x3 = 4.4934

x4 = 4.4549

...

The numerical value for sqrt(2) + 3 is 4.4142, which the method will slowly tend to.

Hope this helps

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