Question

3. By which smallest number should 8232 be multiplied to make it a perfect cube? Find the cube root of the perfect cube. ​

Answer 1

Answer:

To find :

1 )smallest number by which 8232 must be multiplied to obtain a             perfect cube .

2) cube root

3) perfect cube

Solution : Prime factorizing 8232, we get,

8232 =   2 x 2 x 2 x 7 x 7 x 7 x 3

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 3 and number of 7's is also 3 but number of 3's is only 1.

So we need to multiply another two 3's in the factorization to make 8232 a perfect cube.

Hence, the smallest number by which 8232 must be multiplied to obtain a perfect cube is 3 x 3 = 9.

we get perfect cube =  74,088

and cube root = 42

smallest number to be multiplied = 3 x 3 = 9

Answer 2

Given number is $8232$

We have to find a smallest number which multiplied to make a perfect cube.

For this we have to expand the number.

This number $8232$ can also be written as

$2\times2\times2\times3\times7\times7\times7$

From the above

The prime number $2$ is already as a cube

The prime number $7$ is already as a cube

So, now we have to multiply the $3$ two times to make a cube.

So, $9$ is multiplied by the given to make a perfect cube.

$8232\times9$

$74088$

Perfect cube is $74088$

The perfect cube root is $2\times3\times7$

$42$

Therefore, Perfect cube is $74088$.

The perfect cube root is $42$