Question

Find the cube roots of the following numbers :
(i) 729 (ii) 4913 (iii) 117649

Answer 1

(i) 729 The unit digit of 729 is 9. Therefore, the digit at the unit place in the cube root is 9. Since no number is left after striking out the units, tens and hundreds digits of the number, the required cube root is 9.

(ii) 4913 Here, unit digit is 3. Therefore, unit digit of the cube root is 7. After striking out the last three digits from the right, we are left with the number 4. Now 1 is the largest number whose cube is less than 4. Therefore, the ten’s digit is 1.

Thus, the required cube root is 17.

(iii) 117649 Here, unit digit is 9. Therefore, the unit digit of the cube root is 9. Striking out the last three digit from the right, the number left is 117.

Now $4^3=64<117and{5}^3=125>117$.
Hence, the tens digit of the cube root is 4.

$\therefore$ $\sqrt[3]{3117649}=49$