Question

find the smallest no. by which 2560 must be multiplied so that the product is a perfect cube​

Answer 1

The answer is 5!

Since 5 left unpaired, to make perfect cube , we should multiplied 5×5=25 . 2560×25 = 64000. which is a perfect cube. hence the smallest no by which 2560 must be multiplied so that product is perfect cube = 5×5=25

Answer 2

we try to find by prime factorisation

step by step explaination

$\sqrt[3]{2560 }$

2560=

$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5$

clearly for making cube must be multiply by

$5 \times 5$

= 25

both side

$2560 \times 25 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$

hence,

64060=2560 .

ans. = smallest number is 25