Question

prove that (2 +√3) is an irrational number​

Answer 1

Answer: no

Step-by-step explanation:>Answer. Let 2-√3 be rational no. therefore,-√3 is a rational no. ... So,2-√3 is a irrational no.

Answer 2

Answer:

ʙʏ ᴄᴏɴᴛʀᴀᴅɪᴄᴛᴏʀʏ ᴍᴇᴛʜᴏᴅ..

ᴡᴇ ᴀꜱꜱᴜᴍᴇ ᴛʜᴀᴛ 2 + √3 ɪꜱ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

=> 2 + √3 = ᴘ/Q , ᴡʜᴇʀᴇ ᴘ & Q ᴀʀᴇ ɪɴᴛᴇɢᴇʀꜱ, ‘Q’ ɴᴏᴛ = 0.

=> √3 = (ᴘ/Q) - 2

=> √3 = (ᴘ - 2Q)/ Q ………… (1)

=> ʜᴇʀᴇ, ʟʜꜱ √3 ɪꜱ ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

ʙᴜᴛ ʀʜꜱ ɪꜱ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.. ʀᴇᴀꜱᴏɴ- ᴛʜᴇ ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ᴏꜰ 2 ɪɴᴛᴇɢᴇʀꜱ ɪꜱ ᴀʟᴡᴀʏꜱ ᴀɴ ɪɴᴛᴇɢᴇʀ. ꜱᴏ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ (ᴘ- 2Q) ɪꜱ ᴀɴ ɪɴᴛᴇɢᴇʀ.

& ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ‘Q’ ɪꜱ ᴀɴ ɪɴᴛᴇɢᴇʀ.&‘Q’ ɴᴏᴛ = 0

ᴛʜɪꜱ ᴡᴀʏ, ᴀʟʟ ᴄᴏɴᴅɪᴛɪᴏɴꜱ ᴏꜰ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ᴀʀᴇ ꜱᴀᴛɪꜱꜰɪᴇᴅ.

=> ʀʜꜱ (ᴘ- 2Q)/Q ɪꜱ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

ʙᴜᴛ , ʟʜꜱ ɪꜱ ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ.

=> ʟʜꜱ ᴏꜰ….. (1) ɪꜱ ɴᴏᴛ = ʀʜꜱ.

=> ᴏᴜʀ ᴀꜱꜱᴜᴍᴘᴛɪᴏɴ, ᴛʜᴀᴛ 2 + √3 ɪꜱ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ, ɪꜱ ɪɴᴄᴏʀʀᴇᴄᴛ..

=> 2 + √3 ɪꜱ ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ

Step-by-step explanation:

☘️ⱧɆⱠ₱₣ɄⱠ ₣ØⱤ ɎØɄ☘️