Question

6. Find the smallest number by which 8788 should be divided so that quotient is a perfect
cube. Also find the cube root of the quotient.
7. Find the side of a cube whose volume is 4096 m.​

Answer 1

Answer:

6.

Step-by-step explanation:

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, 48788=42×2×13×13×13

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

Thus, the cube root of 2197=13

7.

a≈16

V

Volume Unit Conversion:Using the formula

V=a3

Solving for

aa=V⅓=4096⅓≈16