Question

Which of the following are the cubes of even natural numbers!
1000
Which of the following are the cubes of odd natural numbers?
43 cu 1728 v) 4096
Find the smallest number by which 1823 must be multiplied so that the product is a perfect eube.
Find the least number by which 2560 must be multiplied so that the product is a perfect cube.
7. What is the least number by which 1600 must be divided so that the quotient is a perfect cube?
Find the smallest number by which 8788 must be divided so that the quotient is a perfect cube.​

Answer 1

Answer:

The given number is 8788

The prime factorisation of 8788 is given by,

8788=2×2×13×13×13

We see that prime factor 2 does not occur in the group of 3, hence the given number is not a perfect cube.

In order to make it a perfect cube, it must be divided by 4.

Now,

4

8788

=

4

2×2×13×13×13

⇒2197=13×13×13, which is a perfect cube number.

Thus, the cube root of 2197=13