Question

The number of perfect cubes that lie between 2^9+1 and 2^18+1 is​

Answer 1

Answer:

The number of perfect cubes that lie between $2^{9}+1$ and $2^{18}+1$ is 56.

To find:

The number of perfect cubes that lie between $2^{9}+1$ and $2^{18}+1$.  

Solution:

Let us find the equivalent value of the given expression, $2^{9}+1$ = 512 + 1 = 513,  

(where 512 = $8^3$)

let us find the equivalent value of the given expression, $2^{18}$+1 = 512 + 1 = 262145,  

(where 262145 = $64^3$)

The number of cubes between 513 and 262145 is 64 – 8 = 56 .

Result:

The number of perfect cubes that lie between $2^{9}+1$ and $2^{18}+1$ is 56.