diff --git a/starlette/requests.py b/starlette/requests.py
index 5c7a4296c..83a52aca1 100644
--- a/starlette/requests.py
+++ b/starlette/requests.py
@@ -101,9 +101,7 @@ def base_url(self) -> URL:
             base_url_scope = dict(self.scope)
             base_url_scope["path"] = "/"
             base_url_scope["query_string"] = b""
-            base_url_scope["root_path"] = base_url_scope.get(
-                "app_root_path", base_url_scope.get("root_path", "")
-            )
+            base_url_scope["root_path"] = base_url_scope.get("root_path", "")
             self._base_url = URL(scope=base_url_scope)
         return self._base_url
 
diff --git a/starlette/routing.py b/starlette/routing.py
index cb1b1d919..b167f3513 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -251,8 +251,11 @@ def __init__(
         self.path_regex, self.path_format, self.param_convertors = compile_path(path)
 
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
+        path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] == "http":
-            match = self.path_regex.match(scope["path"])
+            root_path = scope.get("route_root_path", scope.get("root_path", ""))
+            path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
+            match = self.path_regex.match(path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
@@ -338,8 +341,11 @@ def __init__(
         self.path_regex, self.path_format, self.param_convertors = compile_path(path)
 
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
+        path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] == "websocket":
-            match = self.path_regex.match(scope["path"])
+            root_path = scope.get("route_root_path", scope.get("root_path", ""))
+            path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
+            match = self.path_regex.match(path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
@@ -410,23 +416,25 @@ def routes(self) -> typing.List[BaseRoute]:
         return getattr(self._base_app, "routes", [])
 
     def matches(self, scope: Scope) -> typing.Tuple[Match, Scope]:
+        path_params: "typing.Dict[str, typing.Any]"
         if scope["type"] in ("http", "websocket"):
             path = scope["path"]
-            match = self.path_regex.match(path)
+            root_path = scope.get("route_root_path", scope.get("root_path", ""))
+            route_path = scope.get("route_path", re.sub(r"^" + root_path, "", path))
+            match = self.path_regex.match(route_path)
             if match:
                 matched_params = match.groupdict()
                 for key, value in matched_params.items():
                     matched_params[key] = self.param_convertors[key].convert(value)
                 remaining_path = "/" + matched_params.pop("path")
-                matched_path = path[: -len(remaining_path)]
+                matched_path = route_path[: -len(remaining_path)]
                 path_params = dict(scope.get("path_params", {}))
                 path_params.update(matched_params)
                 root_path = scope.get("root_path", "")
                 child_scope = {
                     "path_params": path_params,
-                    "app_root_path": scope.get("app_root_path", root_path),
-                    "root_path": root_path + matched_path,
-                    "path": remaining_path,
+                    "route_root_path": root_path + matched_path,
+                    "route_path": remaining_path,
                     "endpoint": self.app,
                 }
                 return Match.FULL, child_scope
@@ -767,11 +775,15 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
             await partial.handle(scope, receive, send)
             return
 
-        if scope["type"] == "http" and self.redirect_slashes and scope["path"] != "/":
+        root_path = scope.get("route_root_path", scope.get("root_path", ""))
+        path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
+        if scope["type"] == "http" and self.redirect_slashes and path != "/":
             redirect_scope = dict(scope)
-            if scope["path"].endswith("/"):
+            if path.endswith("/"):
+                redirect_scope["route_path"] = path.rstrip("/")
                 redirect_scope["path"] = redirect_scope["path"].rstrip("/")
             else:
+                redirect_scope["route_path"] = path + "/"
                 redirect_scope["path"] = redirect_scope["path"] + "/"
 
             for route in self.routes:
diff --git a/starlette/staticfiles.py b/starlette/staticfiles.py
index 2f1f1ddab..f36d58664 100644
--- a/starlette/staticfiles.py
+++ b/starlette/staticfiles.py
@@ -1,5 +1,6 @@
 import importlib.util
 import os
+import re
 import stat
 import typing
 from email.utils import parsedate
@@ -108,7 +109,9 @@ def get_path(self, scope: Scope) -> str:
         Given the ASGI scope, return the `path` string to serve up,
         with OS specific path separators, and any '..', '.' components removed.
         """
-        return os.path.normpath(os.path.join(*scope["path"].split("/")))  # type: ignore[no-any-return]  # noqa: E501
+        root_path = scope.get("route_root_path", scope.get("root_path", ""))
+        path = scope.get("route_path", re.sub(r"^" + root_path, "", scope["path"]))
+        return os.path.normpath(os.path.join(*path.split("/")))  # type: ignore[no-any-return]  # noqa: E501
 
     async def get_response(self, path: str, scope: Scope) -> Response:
         """
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 7644f5a24..1e99e335b 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -159,7 +159,7 @@ async def websocket_params(session: WebSocket):
 
 
 @pytest.fixture
-def client(test_client_factory):
+def client(test_client_factory: typing.Callable[..., TestClient]):
     with test_client_factory(app) as client:
         yield client
 
@@ -170,7 +170,7 @@ def client(test_client_factory):
     r":UserWarning"
     r":charset_normalizer.api"
 )
-def test_router(client):
+def test_router(client: TestClient):
     response = client.get("/")
     assert response.status_code == 200
     assert response.text == "Hello, world"
@@ -1210,3 +1210,57 @@ async def startup() -> None:
             ...  # pragma: nocover
 
         router.on_event("startup")(startup)
+
+
+async def echo_paths(request: Request, name: str):
+    return JSONResponse(
+        {
+            "name": name,
+            "path": request.scope["path"],
+            "root_path": request.scope["root_path"],
+        }
+    )
+
+
+echo_paths_routes = [
+    Route(
+        "/path",
+        functools.partial(echo_paths, name="path"),
+        name="path",
+        methods=["GET"],
+    ),
+    Mount(
+        "/root",
+        name="mount",
+        routes=[
+            Route(
+                "/path",
+                functools.partial(echo_paths, name="subpath"),
+                name="subpath",
+                methods=["GET"],
+            )
+        ],
+    ),
+]
+
+
+def test_paths_with_root_path(test_client_factory: typing.Callable[..., TestClient]):
+    app = Starlette(routes=echo_paths_routes)
+    client = test_client_factory(
+        app, base_url="https://www.example.org/", root_path="/root"
+    )
+    response = client.get("/root/path")
+    assert response.status_code == 200
+    assert response.json() == {
+        "name": "path",
+        "path": "/root/path",
+        "root_path": "/root",
+    }
+
+    response = client.get("/root/root/path")
+    assert response.status_code == 200
+    assert response.json() == {
+        "name": "subpath",
+        "path": "/root/root/path",
+        "root_path": "/root",
+    }