It took us until the 80th problem to find one, but we finally found an ugly wart in Clojure 1.2: big square roots. At the time of writing, it does not properly accommodate bigdec numbers. Look at this ugly behavior:

(expt 12 34)       ;; 4922235242952026704037113243122008064 ... a bignum.
(expt 12 (/ 34))   ;; 1.0758225047262997                    ... a double!
(with-precision 100 (expt 12 (/ 34))) ;;  1.0758225047262997... still a double!

Anyway, as I borrowed a little code to quickly implement a big-sqrt function but since I am not sure about the copyright of the code in question, I leave that function as an exercise to the reader. Accomplishing the task via Java libraries is another option.

With the big-sqrt function out of the way, the rest of this problem was extremely straightforward.

(use '[clojure.contrib.math :only (sqrt expt)])

(defn big-sqrt [n]
  (with-precision 150 (exercise-for-the-reader)))

(defn as-digits [num]
  (filter #(>= % 0) (map #(Character/getNumericValue %) (str num))))

(defn hundred-digit-sum [num]
  (reduce + (take 100 (as-digits num))))

(defn square? [n] (= n (* (int (sqrt n)) (int (sqrt n)))))

(defn euler-80 []
  (->> (for [n (range 1 101)
             :when (not (square? n))]
         (hundred-digit-sum (big-sqrt (bigdec n))))
       (reduce +)))

(time (euler-80)) ;; "Elapsed time: 92.808923 msecs"