Find the tens digit of the cube root of each of the numbers in Q. No. 15.

Solution:

(i) Let us consider the number 226981.

The unit digit is 1; therefore, the unit digit of the cube root of 226981 is 1.

After striking out the units, tens and hundreds digits of the given number, we are left with 226.

Now, 6 is the largest number, whose cube is less than or equal to $226\left(6^{3}<226<7^{3}\right)$.

Therefore, the tens digit of the cube root of 226981 is 6.

(ii) Let us consider the number 13824.

The unit digit is 4; therefore, the unit digit of the cube root of 13824 is 4.

After striking out the units, tens and hundreds digits of the given number, we are left with 13.

Now, 2 is the largest number, whose cube is less than or equal to $13\left(2^{3}<13<3^{3}\right)$.

Therefore, the tens digit of the cube root of 13824 is 2.

(iii) Let us consider the number 571787.

The unit digit is 7; therefore, the unit digit of the cube root of 571787 is 3.

After striking out the units, tens and hundreds digits of the given number, we are left with 571.

Now, 8 is the largest number, whose cube is less than or equal to $571\left(8^{3}<571<9^{3}\right)$.

Therefore, the tens digit of the cube root of 571787 is 8.

(iv) Let us consider the number 175616.

The unit digit is 6; therefore, the unit digit of the cube root of 175616 is 6.

After striking out the units, tens and hundreds digits of the given number, we are left with 175.

Now, 5 is the largest number, whose cube is less than or equal to $175\left(5^{3}<175<6^{3}\right)$

Therefore, the tens digit of the cube root of 175616 is 5.