The Maggid Mishnah in Hilchos Shabbos (17:26) says that one may rely on π=3
It actually is commenting on the Rambam's statement that a circle of circumference three has diameter one. It says that that's "not precise…, but the rabbis were not careful about things that are only required by rabbinical ordinance, and were lenient about it".
he says in Hilchos Eiruvin (3:2) that one may not rely on √2=1.4.
It is commenting on the Talmud's statement that a circle of circumference 16.8 is big enough to contain a four-by-four square. In fact, even if we divide by just 3, that's not quite big enough for a four-by-four square unless we assume a four-by-four square has diagonal 4×1.4, in which case it's exactly right. So the מגיד משנה comments that the 16.8 "number is not exact, which is why Rambam [omitted it, and instead] wrote [only] 'if there's enough to contain a four-by-four square'". So we see that he holds Rambam is not willing to rely on the 1.4 approximation.
But those seem to be his views of what Rambam holds, rather than his own views like you quoted.
(Both translations are my own, and loose.)
I just realized (h/t Double AA) that what you asked for is "the actual words which convey these points", which I haven't provided. They are:
שמה שאמרו אם היה הקיפה ג׳ טפחים יש בה רחב טפח אינו מדוקדק בחשבון אלא פחות מטפח הוא כחלק מכ״ב על דרך הקרוב ולא דקדקו בשל דבריהם והקילו בו
חלון עגול צריך שיהא בהיקפו כ״ד טפחים ושנים ומשהו מהן בתוך עשרה שאם ירבענו נמצא משהו מהן בתוך עשרה ודקדקו שם בחשבון זה והעלו דבשבסר נכי חומשא סגיא וגם זה החשבון אינו מדוקדק בכוון ולזה כתב רבינו אם יש בו כדי לרבע