Question

The least number of numbers to be deleted from the set[1,2,3,.. .. .. 13,14,15]so that the product of the remaining numbers is a perfect square.

✘ɴᴏ ᴄᴏᴘɪᴇᴅ ᴀɴsᴡᴇʀ
✘ɴᴏ sᴘᴀᴍ​

Answer 1

ǫᴜᴇsᴛɪᴏɴ:—

ᴛʜᴇ ʟᴇᴀsᴛ ɴᴏ ᴏғ ɴᴏ's ᴛᴏ ʙᴇ ᴅᴇʟᴇᴛᴇᴅ ғʀᴏᴍ ᴛʜᴇ sᴇᴛ[1,2,3,.. .. ..13,14,15]sᴏ ᴛʜᴀᴛ ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ɴᴏ's ɪs ᴀ ᴘᴇʀғᴇᴄᴛ sǫᴜᴀʀᴇ.

ᴀɴsᴡᴇʀ:—

$1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 13 \times 14 \times 15$

ɪɴ ᴛʜᴇ sᴇᴛ [1×2×3×.. .. ..×13×14×15] ɪ ғᴏᴜɴᴅ ᴛʜᴀᴛ ᴛʜᴇʀᴇ ᴀʀᴇ ɴᴏ's ɪɴ ᴛʜᴇ ᴘᴏᴡᴇʀ ᴏғ 2,3,5,7,11..

ɪɴ ᴛʜɪs sᴇᴛ :

ғᴏʟʟᴏᴡɪɴɢ ᴘᴏᴡᴇʀs ᴀʀᴇ ᴀs ғᴏʟʟᴏᴡs:

ᴛʜᴇʀᴇ ᴀʀᴇ 2¹¹

$= {3}^{6} \\ = {5}^{3} \\ = {7}^{2} \\ = {11}^{1}$

sᴏ ɪғ ɪ ʀᴇᴍᴏᴠᴇ 2,5,11 ᴀɴᴅ 13 sᴏ ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ɴᴏ ᴡɪʟʟ ʙᴇ ᴀ ᴘᴇʀғᴇᴄᴛ sǫᴜᴀʀᴇ.

ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ʀᴇᴍᴏᴠᴇ ᴛʜᴇ ʟᴇᴀsᴛ ɴᴏ sᴏ ɪғ ɪ ᴍᴜʟᴛɪᴘʟʏ 2 ᴀɴᴅ 5 =10

sᴏ, ɪ ʜᴀᴠᴇ ᴛᴏ ʀᴇᴍᴏᴠᴇ ᴏɴʟʏ 3 ɴᴜᴍʙᴇʀs ᴛʜᴀᴛ ᴀʀᴇ 10,11,13..

ʜᴏᴘᴇ ᴛʜɪs ʜᴇʟᴘs ʏᴏᴜ

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Answer 2

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