Cube root of 4096 is

Question

Accepted Answer

To determine the cube root of 4096, we need to find a number which, when multiplied by itself three times (cubed), equals 4096. The correct answer is Option 3: 16. Let's break down why this is the case and why the other options are incorrect.

1. **Explanation for Option 3 (16):**
   - To verify that 16 is the cube root of 4096, we calculate $16^3$.
   - $16 \times 16 = 256$.
   - $256 \times 16 = 4096$.
   - Therefore, $16^3 = 4096$, confirming that the cube root of 4096 is indeed 16.

2. **Why Option 1 (24) is incorrect:**
   - If 24 were the cube root of 4096, then $24^3$ should equal 4096.
   - $24 \times 24 = 576$.
   - $576 \times 24 = 13824$.
   - Since 13824 is not equal to 4096, 24 is not the cube root of 4096.

3. **Why Option 2 (14) is incorrect:**
   - If 14 were the cube root of 4096, then $14^3$ should equal 4096.
   - $14 \times 14 = 196$.
   - $196 \times 14 = 2744$.
   - Since 2744 is not equal to 4096, 14 is not the cube root of 4096.

4. **Why Option 4 (12) is incorrect:**
   - If 12 were the cube root of 4096, then $12^3$ should equal 4096.
   - $12 \times 12 = 144$.
   - $144 \times 12 = 1728$.
   - Since 1728 is not equal to 4096, 12 is not the cube root of 4096.

In conclusion, the only number that satisfies the condition of being the cube root of 4096 is 16, making Option 3 the correct answer.