Question

Show that 13 is not rational​

Answer 1

Answer:

The rational root theorem guarantees its roots aren't rational and since √13 is a root of the polynomial, it is irrational. Let √p=mn where m,n∈N. and m and n have no factors in common. So mn can not exist and the square root of any prime is irrational.

Answer 2

ᴀɴsᴡᴇʀ ⤵️

➡️ᴛʜᴇ ʀᴀᴛɪᴏɴᴀʟ ʀᴏᴏᴛ ᴛʜᴇᴏʀᴇᴍ ɢᴜᴀʀᴀɴᴛᴇᴇs ɪᴛs ʀᴏᴏᴛs ᴀʀᴇɴ'ᴛ ʀᴀᴛɪᴏɴᴀʟ ᴀɴᴅ sɪɴᴄᴇ √13 ɪs ᴀ ʀᴏᴏᴛ ᴏғ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ, ɪᴛ ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ. ʟᴇᴛ √ᴘ=ᴍɴ ᴡʜᴇʀᴇ ᴍ,ɴ∈ɴ. ᴀɴᴅ ᴍ ᴀɴᴅ ɴ ʜᴀᴠᴇ ɴᴏ ғᴀᴄᴛᴏʀs ɪɴ ᴄᴏᴍᴍᴏɴ. sᴏ ᴍɴ ᴄᴀɴ ɴᴏᴛ ᴇxɪsᴛ ᴀɴᴅ ᴛʜᴇ sϙᴜᴀʀᴇ ʀᴏᴏᴛ ᴏғ ᴀɴʏ ᴘʀɪᴍᴇ ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.

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