Question

Show that 3+2√5 is an irrational number.​

Answer 1

ᎪΝՏᏔᎬᎡ -

Pʀᴏᴠᴇ 3+25 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.

→ ʟᴇᴛ ᴛᴀᴋᴇ ᴛʜᴀᴛ 3+25 ɪs ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ

→ sᴏ, ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ᴛʜɪs ᴀɴsᴡᴇʀ ᴀs

⇒3+25=ʙᴀ 

Hᴇʀᴇ ᴀ & ʙ ᴜsᴇ ᴛᴡᴏ ᴄᴏᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ ᴀɴᴅ ʙ=0.

⇒25=ʙᴀ−3

⇒25=ʙᴀ−3ʙ

∴5=2ʙᴀ−3ʙ

Hᴇʀᴇ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ɪɴᴛᴇɢᴇʀ sᴏ 2ʙᴀ−3ʙ ɪs ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ sᴏ 5 sʜᴏᴜʟᴅ ʙᴇ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ʙᴜᴛ

5 ɪs ᴀ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ sᴏ ɪᴛ ɪs ᴄᴏɴᴛʀᴀᴅɪᴄᴛ

- Hᴇɴᴄᴇ 3+25 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.

HOPE IT HELPS YOU.!

HAVE A GREAT DAY AHEAD.!!