Question

prove that ✓3is not rational number​

Answer 1

Step-by-step explanation:

Since both q and r are odd, we can write q=2m−1 and r=2n−1 for some m,n∈N. ... Therefore there exists no rational number r such that r2=3. Hence the root of 3 is an irrational number.

Answer 2

Answer:

sɪɴᴄᴇ ʙᴏᴛʜ ǫ ᴀɴᴅ ʀ ᴀʀᴇ ᴏᴅᴅ, ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ǫ=2ᴍ−1 ᴀɴᴅ ʀ=2ɴ-1 ғᴏʀ sᴏᴍᴇ ᴍ,ɴ∈ɴ. ... ᴛʜᴇʀᴇғᴏʀᴇ ᴛʜᴇʀᴇ ᴇxɪsᴛs ɴᴏ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ʀ sᴜᴄʜ ᴛʜᴀᴛ ʀ2=3. ʜᴇɴᴄᴇ ᴛʜᴇ ʀᴏᴏᴛ ᴏғ ɪs ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.