diff --git a/eval.c b/eval.c
index 08a7e0a7..2ec932f5 100644
--- a/eval.c
+++ b/eval.c
@@ -1088,7 +1088,7 @@ static sexp sexp_sqrt (sexp ctx sexp_api_params(self, n), sexp z) {
   else
     return sexp_type_exception(ctx, self, SEXP_NUMBER, z);
   r = sqrt(d);
-  if (sexp_fixnump(z) && ((r*r) == (double)sexp_unbox_fixnum(z)))
+  if (sexp_fixnump(z) && (((sexp_uint_t)r*(sexp_uint_t)r)==sexp_unbox_fixnum(z)))
     return sexp_make_fixnum(round(r));
   else
     return sexp_make_flonum(ctx, r);
diff --git a/lib/init.scm b/lib/init.scm
index 8ea2077b..d71570b5 100644
--- a/lib/init.scm
+++ b/lib/init.scm
@@ -419,8 +419,16 @@
 (define real? number?)
 (define (exact? x) (if (fixnum? x) #t (bignum? x)))
 (define inexact? flonum?)
+(define (exact-integer? x) (if (fixnum? x) #t (bignum? x)))
 (define (integer? x)
-  (if (fixnum? x) #t (if (bignum? x) #t (and (flonum? x) (= x (truncate x))))))
+  (if (exact-integer? x) #t (and (flonum? x) (= x (truncate x)))))
+
+(define (exact-integer-sqrt x)
+  (let ((res (sqrt x)))
+    (if (exact? res)
+        (values res 0)
+        (let ((res (inexact->exact (truncate res))))
+          (values res (- x (* res res)))))))
 
 (define (zero? x) (= x 0))
 (define (positive? x) (> x 0))