Multiply 210125 by the smallest no. so that the product is a cube. Also, find the cube of the quotient.
Answers
Answer: 41 and 205
Step-by-step explanation:
On factorising 210125 into prime factors, we get: 210125 = 5 x 5 x 5 x 41 x 41
On grouping the factors in triples of equal factors, we get: 210125 = {5 x 5 x 5 x 41 x 41}
It is evident that the prime factors of 210125 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 210125 is not a perfect cube. However, if the number is multiplied by 41, the factors can be grouped into triples of equal factors such that no factor is left over.
Hence, the number 210125 should be multiplied by 41 to make it a perfect cube.
Also, the product is given as: 210125 x 41 = {5 x 5 x 5} x {41 x 41 x 41}
8615125 = {5 x 5 x x {41 x 41 x 41}
To get the cube root of the produce 8615125, take one factor from each triple.
The cube root is 5 x 41 = 205. Hence, the required numbers are 41 and 205.
Answer:multiply by 41 and cube root is 205
Step-by-step explanation:
as we know for being a number to cube it must have thrice of prime numbers in its factor. if it have thrice then it is called a perfect cube and if not then it is not a perfect cube.
factor of 210125 is
210125 = 5*5 * 5*41*41
it have a thrice of 5 but a pair of 41.
to make it perfect cube we have to multiply by 41.
smallest number so that mutiply by the number product is a perfect cube is 41
and cube root of 210125 is 5*41= 205