Find the value of sqrt[3]117649 .

The correct answer is Option (2) → 49

For a perfect cube, the last digit of the number fixes the last digit of its cube root, and the digits left after removing the last three fix the rest of the root.

117649 ends in 9, and only a number ending in 9 has a cube ending in 9 (\(9^{3}=729\)), so the root ends in 9.

Removing the last three digits leaves 117, which lies between \(4^{3}=64\) and \(5^{3}=125\), so the tens digit is 4.

Cube root = 49