Is the square root of 14 rational?

1 Answer
Sep 30, 2015

Answer:

No, #sqrt(14) = sqrt(2*7)# is irrational for the same reasons that #sqrt(15)# is irrational.

Explanation:

http://socratic.org/questions/how-do-you-prove-that-square-root-15-is-irrational

See my proof for #sqrt(15)#.

If the radicand (the expression under the square root sign) only has perfect square factors then the square root is rational. Otherwise it will be irrational.