Question

find the smallest no. which when multiplied with 137592 will make the product a perfect cube​

Answer 1

Step-by-step explanation:

1183

here it is clear that when we multiply 137592 by the number 7 × 13² we get, 2³ × 3³ × 7² × 13 × 7 × 13² = (2 × 3 × 7 × 13)³ ⇒a perfect cube. Therefore the smallest number is 1183 and the cube root of the product is 546

Answer 2

1183

ʜᴇʀᴇ ɪᴛ ɪs ᴄʟᴇᴀʀ ᴛʜᴀᴛ ᴡʜᴇɴ ᴡᴇ ᴍᴜʟᴛɪᴘʟʏ 137592 ʙʏ ᴛʜᴇ ɴᴜᴍʙᴇʀ 7 × 13²

ᴡᴇ ɢᴇᴛ, 2³ × 3³ × 7² × 13 × 7 × 13² = (2 × 3 × 7 × 13)³ ⇒ᴀ ᴘᴇʀғᴇᴄᴛ ᴄᴜʙᴇ.

ᴛʜᴇʀᴇғᴏʀᴇ

ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ ɪs 1183 ᴀɴᴅ ᴛʜᴇ ᴄᴜʙᴇ ʀᴏᴏᴛ ᴏғ ᴛʜᴇ ᴘʀᴏᴅᴜᴄᴛ ɪs 546