Square root problem

Question

Both the square root of 58 and the square root of 58.01 are irrational numbers. Find a rational number, n, such that the square root of 58 is less than the square root of n which is less than the square root of 58.01

Answer 1

y = √x is an increasing function, so, if 58 < n < 58.01, then                    √58 < √n < √ 58.01.  For example, let n = 58.005.  Then n is rational and satisfies the desired inequality.