A Sanskrit class conducted in Sanskrit needs only a few dozen sentences, and they are a pleasure to use because they are so compact. A single verb form is a whole polite request: आगच्छतु, "please come"; उपविशतु, "please sit".
This ending, -अतु, is the request form that goes with the respectful भवान् or भवती. It is the right form for a teacher, an elder or a stranger, and teachers use it to students too. To several people it becomes -अन्तु: सर्वे उपविशन्तु, "everybody please sit". The bare command to one friend drops the ending: आगच्छ, उपविश, पठ.
The other key word is कृपया, "kindly", the same word that Hindi uses. And for "sorry", Sanskrit says क्षम्यताम्, "may it be forgiven".
आगच्छतु।
āgachchhatu.
आइए।
Please come.
उपविशतु।
upavishatu.
बैठिए।
Please sit down.
उत्तिष्ठतु।
uttishthatu.
खड़े होइए।
Please stand up.
कृपया पुनः वदतु।
kripayā punah vadatu.
कृपया फिर से बोलिए।
Please say it again.
शनैः वदतु।
shanaih vadatu.
धीरे बोलिए।
Please speak slowly.
पुस्तकम् उद्घाटयतु।
pustakam udghātayatu.
पुस्तक खोलिए।
Please open the book.
पठतु।
pathatu.
पढ़िए।
Please read.
लिखतु।
likhatu.
लिखिए।
Please write.
अहं न जानामि।
aham na jānāmi.
मुझे नहीं पता।
I do not know.
अहं न अवगच्छामि।
aham na avagachchhāmi.
मुझे समझ नहीं आया।
I do not understand.
एकः प्रश्नः अस्ति।
ekah prashnah asti.
एक प्रश्न है।
I have a question.
अस्य अर्थः कः?
asya arthah kah?
इसका अर्थ क्या है?
What is the meaning of this?
क्षम्यताम्।
kshamyatām.
क्षमा कीजिए।
Excuse me; I am sorry.
चिन्ता मास्तु।
chintā māstu.
चिंता मत कीजिए।
Do not worry.
अस्तु।
astu.
ठीक है।
All right; so be it.
आम्। / न।
ām, / na.
हाँ। / नहीं।
Yes. / No.
बहु शोभनम्।
bahu shobhanam.
बहुत अच्छा।
Very good.
सम्यक् उक्तम्।
samyak uktam.
ठीक कहा।
Well said.
किम् अहम् अन्तः आगच्छानि?
kim aham antah āgachchhāni?
क्या मैं अंदर आ सकता हूँ?
May I come in?
श्वः मिलामः।
shvah milāmah.
कल मिलते हैं।
See you tomorrow.
Asking questions
Sanskrit question words begin with क, as Hindi ones do: किम् (what), कः / का (who, masculine and feminine), कुत्र (where), कदा (when), कथम् (how), किमर्थम् (why), कति (how many). A yes-or-no question puts किम् first, like the Hindi क्या: किं भवान् संस्कृतं जानाति?, "Do you know Sanskrit?" The answer is आम्, जानामि or न जानामि.
More of these small unchanging words are on the avyaya page.