Find the shortcut

since cube of 3 brings the last digit as 7 => last digit of the cube root is 3. now, $5^{3}=125\;=>50^{3}=125000<148877$ $6^{3}=216\;=>60^{3}=216000>148877$ so, it lies between 50 and 60. only possible is 53 since its last digit is 3. so 53

The answer is 53. If 5^3 = 125,then 50^3 = 125,000. Similarly, 60^3 = 216,000.Note that 148,877 is in between 125,000 and 216,000,so if 148,877 is the cube of some whole number, that number must between 50 and 60. But the only way the cube of a number can end in 7 is if the original number ends in 3.(In particular, 3^3 equals 27. The general pattern can be checked by trial and error: The cube of a number ending in 1 also ends in 1, the cube of a number ending in 2 ends in 8, and so on.) Therefore the cube root of 148,877 must be 53.

make groups of 3 digits from the end you must know in case of cube of 0, 1, 4, 5, 6 ends with same digit as 0, 1, 4, 5, 6 respectively cube of 2 and 8 interchange similarly cube of 3 and 7 interchange.

No = 148877 make groups of 3 digits from the end as 148 877 so cube root ends with 3 (from last 3 digits 877)

consider group 1 having 148 a number whose cube is 148 or less than 148 is 5³ as 125 < 148 < 216

so answer is 53³ = 148877