Find the cube root of 46656 :

Question

Accepted Answer

To find the cube root of 46656, we need to determine which number, when multiplied by itself three times (cubed), equals 46656. Let's evaluate each option:

1. **Option 1: 26**
   - Calculating $26^3$: 
     $$
     26 \times 26 \times 26 = 26 \times 676 = 17576
     $$
   - The result, 17576, is not equal to 46656. Therefore, Option 1 is incorrect.

2. **Option 2: 36**
   - Calculating $36^3$:
     $$
     36 \times 36 \times 36 = 36 \times 1296 = 46656
     $$
   - The result, 46656, matches the number we are finding the cube root for. Therefore, Option 2 is correct.

3. **Option 3: 34**
   - Calculating $34^3$:
     $$
     34 \times 34 \times 34 = 34 \times 1156 = 39304
     $$
   - The result, 39304, is not equal to 46656. Therefore, Option 3 is incorrect.

4. **Option 4: 46**
   - Calculating $46^3$:
     $$
     46 \times 46 \times 46 = 46 \times 2116 = 97336
     $$
   - The result, 97336, is not equal to 46656. Therefore, Option 4 is incorrect.

In conclusion, the only option that satisfies the condition of being the cube root of 46656 is Option 2, which is 36. This is why Option 2 is the correct answer.