What is the square root of 13?

Answer 1

Go 3.25 units of distance in any direction. Turn 90 degrees clockwise and go 3.25 units of distance in a straight line. Turn 90 degrees clockwise and go 3.25 units of distance in a straight line. Turn 90 degrees clockwise and go 3.25 units of distance in a straight line.

You will have travelled along a square route whose total distance is 13 units. Alternatively you could have turned counter clockwise each time.

Answer 2

± 3.605551275464

Since 13 is not a square number there is no exact real answer, but you can find an approximate value using the following (Newton-Raphson) iteration formula:

xn+1=xn - (x2n -13)/(2xn)

Using this formula the square root of 13 can be stated as 3.605551275 to 10 s.f. after 3 iterations starting from 3.5. Further iterations would yield even more accurate solutions to more significant figures. Alternatively, just use a calculator.