Question

Let P be a prime number if P divides a2 then p and a are co primes or P divides under root a or P divides a or a divides p.

Answer 1

Step-by-step explanation:

a divides p

mark as BRAINLIEST pls pls p!s

Answer 2

ɪғ ᴘᴏssɪʙʟᴇ,ʟᴇᴛ √ᴘ ʙᴇ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

ᴀʟsᴏ ᴀ ᴀɴᴅ ʙ ɪs ʀᴀᴛɪᴏɴᴀʟ.

ᴛʜᴇɴ,√ᴘ = ᴀ/ʙ

ᴏɴ sϙᴜᴀʀɪɴɢ ʙᴏᴛʜ sɪᴅᴇs,ᴡᴇ ɢᴇᴛ,

(√ᴘ)²= ᴀ²/ʙ²

→ᴘ = ᴀ²/ʙ²

→ʙ² = ᴀ²/ᴘ [ᴘ ᴅɪᴠɪᴅᴇs ᴀ² sᴏ,ᴘ ᴅɪᴠɪᴅᴇs ᴀ]

ʟᴇᴛ ᴀ= ᴘʀ ғᴏʀ sᴏᴍᴇ ɪɴᴛᴇɢᴇʀ ʀ

→ʙ² = (ᴘʀ)²/ᴘ

→ʙ² = ᴘ²ʀ²/ᴘ

→ʙ² = ᴘʀ²

→ʀ² = ʙ²/ᴘ [ᴘ ᴅɪᴠɪᴅᴇs ʙ² sᴏ, ᴘ ᴅɪᴠɪᴅᴇs ʙ]

ᴛʜᴜs ᴘ ɪs ᴀ ᴄᴏᴍᴍᴏɴ ғᴀᴄᴛᴏʀ ᴏғ ᴀ ᴀɴᴅ ʙ.

ʙᴜᴛ ᴛʜɪs ɪs ᴀ ᴄᴏɴᴛʀᴀᴅɪᴄᴛɪᴏɴ, sɪɴᴄᴇ ᴀ ᴀɴᴅ ʙ ʜᴀᴠᴇ ɴᴏ ᴄᴏᴍᴍᴏɴ ғᴀᴄᴛᴏʀ.

ᴛʜɪs ᴄᴏɴᴛʀᴀᴅɪᴄᴛɪᴏɴ ᴀʀɪsᴇs ʙʏ ᴀssᴜᴍɪɴɢ √ᴘ ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

ʜᴇɴᴄᴇ,√ᴘ ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.