# How Do You Find The Exact Value Of Square Root of 3, 5, 7, 11?

Is there any method to find the exact value of the square root of 3,5,7,11,13,14,15,17,18, etc.?

Thank you

SteamKing
Staff Emeritus
Homework Helper
Arithmetic algorithms can approximate these square roots, but because they are all irrational, the decimal representations are non-repeating and non-terminating.

HallsofIvy
Homework Helper
The exact values of the square root of 2, 3, 5 ,7, 11, etc are $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, $\sqrt{7}$, $\sqrt{11}$. That's the best you can do. As SteamKing said, all of those, and, in fact, the square root of any integer that is not a "perfect square", are irrational- they cannot be written as a terminating decimal, they cannot be written as a repeating decimal like "0.14141414...", and cannot be written as a fraction (integer over integer).

(I added "2" to the beginning of your list. I am surprized you did not have it.)

Mark44
Mentor
Might as well add 6, 8, 10, and so on to the list, since none of these is a perfect square, and consequently does not have a square root that is rational.

lavinia