The number of digits in the cube root of 6859 is

The number of digits in the cube root of 6859 is

The correct answer and explanation is:

Correct Answer: 1

To find the number of digits in the cube root of 6859, the first step is to determine the cube root of the number.

6859 is a perfect cube, and calculating the cube root directly gives: 68593=19\sqrt[3]{6859} = 19

This can be verified by multiplying: 19×19=36119 \times 19 = 361 361×19=6859361 \times 19 = 6859

So, the cube root of 6859 is 19. The next step is to determine how many digits are in 19. A digit refers to each individual number place in a whole number. The number 19 has two digits: 1 and 9.

Therefore, the correct number of digits in the cube root of 6859 is 2, not 1.

Now, to understand the reasoning more generally, the number of digits in a whole number nn can be found using logarithms: Number of digits in n=⌊log⁡10(n)⌋+1\text{Number of digits in } n = \lfloor \log_{10}(n) \rfloor + 1

For 19: log⁡10(19)≈1.2788\log_{10}(19) \approx 1.2788 ⌊1.2788⌋+1=2\lfloor 1.2788 \rfloor + 1 = 2

So 19 has 2 digits.

The cube root of a number reduces its size significantly. If a number has 4 digits, such as 6859, then its cube root will likely have fewer digits. This is because raising a number to the power of 3 increases its digit length rapidly. Conversely, taking the cube root reduces the number of digits.

In conclusion, the cube root of 6859 is 19, and the number 19 has 2 digits. Therefore, the number of digits in the cube root of 6859 is 2.