Find the cube root of 13824

Question

Accepted Answer

To determine the cube root of 13824, we need to find a number which, when multiplied by itself three times (cubed), equals 13824. The correct answer is given as Option 4, which is 24. Let's verify this and explain why the other options are incorrect.

1. **Verification of Option 4 (24):**
   - Calculate $24^3$:
     $$
     24 \times 24 = 576
     $$
     $$
     576 \times 24 = 13824
     $$
   - Therefore, the cube of 24 is indeed 13824, confirming that the cube root of 13824 is 24. This supports Option 4 as the correct answer.

2. **Explanation of why other options are incorrect:**

- **Option 1 (17):**
     - Calculate $17^3$:
       $$
       17 \times 17 = 289
       $$
       $$
       289 \times 17 = 4913
       $$
     - The cube of 17 is 4913, which is significantly less than 13824. Therefore, Option 1 is incorrect.

- **Option 2 (18):**
     - Calculate $18^3$:
       $$
       18 \times 18 = 324
       $$
       $$
       324 \times 18 = 5832
       $$
     - The cube of 18 is 5832, which is also less than 13824. Therefore, Option 2 is incorrect.

- **Option 3 (28):**
     - Calculate $28^3$:
       $$
       28 \times 28 = 784
       $$
       $$
       784 \times 28 = 21952
       $$
     - The cube of 28 is 21952, which is greater than 13824. Therefore, Option 3 is incorrect.

In conclusion, the only option that satisfies the condition of being the cube root of 13824 is Option 4 (24). This thorough verification confirms that Option 4 is indeed the correct answer.