Cubes can be built by adding blocks of consecutive odd numbers: 1 = 1^3, then 3 + 5 = 8 = 2^3, then 7 + 9 + 11 = 27 = 3^3. The next block 13 + 15 + 17 + 19 = 64 is the cube of which number?

Question

Accepted Answer

4. 64 = 4^3, so it is the cube of 4. Each cube n^3 is the sum of the next n consecutive odd numbers (here 4 odd numbers give 4^3).

Cubes can be built by adding blocks of consecutive odd numbers: $1 = 1^{3}$ , then $3 + 5 = 8 = 2^{3}$ , then $7 + 9 + 11 = 27 = 3^{3}$ . The next block 13 + 15 + 17 + 19 = 64 is the cube of which number?

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More Class 8 Patterns in Cubes practice

Cubes can be built by adding blocks of consecutive odd numbers: 1=13, then 3+5=8=23, then 7+9+11=27=33. The next block 13 + 15 + 17 + 19 = 64 is the cube of which number?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Patterns in Cubes practice

Cubes can be built by adding blocks of consecutive odd numbers: $1 = 1^{3}$ , then $3 + 5 = 8 = 2^{3}$ , then $7 + 9 + 11 = 27 = 3^{3}$ . The next block 13 + 15 + 17 + 19 = 64 is the cube of which number?