diff --git a/r/R/arrow-datum.R b/r/R/arrow-datum.R
index 4ec5f8f9d65..39362628bb4 100644
--- a/r/R/arrow-datum.R
+++ b/r/R/arrow-datum.R
@@ -123,7 +123,7 @@ Math.ArrowDatum <- function(x, ..., base = exp(1), digits = 0) {
       x,
       options = list(ndigits = digits, round_mode = RoundMode$HALF_TO_EVEN)
     ),
-    sqrt = eval_array_expression("power_checked", x, 0.5),
+    sqrt = eval_array_expression("sqrt_checked", x),
     exp = eval_array_expression("power_checked", exp(1), x),
     signif = ,
     expm1 = ,
diff --git a/r/R/dplyr-funcs-math.R b/r/R/dplyr-funcs-math.R
index b92c202d048..0ba2ddc856e 100644
--- a/r/R/dplyr-funcs-math.R
+++ b/r/R/dplyr-funcs-math.R
@@ -80,4 +80,19 @@ register_bindings_math <- function() {
       options = list(ndigits = digits, round_mode = RoundMode$HALF_TO_EVEN)
     )
   })
+
+  register_binding("sqrt", function(x) {
+    build_expr(
+      "sqrt_checked",
+      x
+    )
+  })
+
+  register_binding("exp", function(x) {
+    build_expr(
+      "power_checked",
+      exp(1),
+      x
+    )
+  })
 }
diff --git a/r/tests/testthat/test-dplyr-funcs-math.R b/r/tests/testthat/test-dplyr-funcs-math.R
index dd982c99428..47a9f0b7c02 100644
--- a/r/tests/testthat/test-dplyr-funcs-math.R
+++ b/r/tests/testthat/test-dplyr-funcs-math.R
@@ -330,3 +330,25 @@ test_that("floor division maintains type consistency with R", {
     df
   )
 })
+
+test_that("exp()", {
+  df <- tibble(x = c(1:5, NA))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = exp(x)) %>%
+      collect(),
+    df
+  )
+})
+
+test_that("sqrt()", {
+  df <- tibble(x = c(1:5, NA))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = sqrt(x)) %>%
+      collect(),
+    df
+  )
+})