Question

Find the smallest number by which each of the following numbers

must be multiplied to obtain a perfect cube.

a. 2808

b. 1323

c. 128625

d. 13720

e. 68600​

Answer 1

Answer:

e) 68600 is not a perfect cube. To make it a perfect cube we multiply it by 5. Thus, 68600 × 5 = 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7 = 343000, which is a perfect cube. Observe that 343 is a perfect cube.

b) In order for 1323 to become a perfect cube, we need to multiply it by 7. This will give us 9261 and the cube root will be 21. On dividing 1323 by 3 and 7 we get 3 x 3 x 3 x 7 x 7.

Answer 2

Answer:

hope it is helpful...

Step-by-step explanation:

1)2808

So, 2808=2×2×2×3×3×3×13×k . So, for 2808k to be a perfect cube k must have two prime factors as 13 and k will be least if k=132=169.

2)1323

In order for 1323 to become a perfect cube, we need to multiply it by 7. This will give us 9261 and the cube root will be 21. On dividing 1323 by 3 and 7 we get 3 x 3 x 3 x 7 x 7. This shows that a 7 is required to make this number a perfect cube.

3)128625

128625=5×5×5×3×7×7×7

the number 3, should be multiplied twice so that it can form a perfect cube.

the smallest number which 128625 should be multiplied is 3×3×=9

4)13720

13730=2×2×2×5×7×7×7×

we can see that the number 5 is cube

form so to optain a perfect number with which it should be multiplied is 5 .

13720×5=68600.

5)68600

In this factorisation, we find that there is no triplet of 5. So, 68600 is not a perfect cube. To make it a perfect cube we multiply it by 5. Thus, 68600 × 5 = 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7 = 343000, which is a perfect cube.