# What is the Square root of 21?

##### 1 Answer

#### Explanation:

#sqrt(21) ~~ 4.58257569495584000658#

It is expressible as a repeating continued fraction:

#sqrt(21) = [4;bar(1,1,2,1,1,8)] = 4 + 1/(1+1/(1+1/(2+...)))#

To see how to calculate this see http://socratic.org/questions/given-an-integer-n-is-there-an-efficient-way-to-find-integers-p-q-such-that-abs-#176764

We can get a good approximation for

#sqrt(21) ~~ [4;1,1,2,1,1] = 4+1/(1+1/(1+1/(2+1/(1+1/1)))) = 55/12 = 4.58dot(3)#

This is a good approximation because