FIND THE CUBE ROOTS BY ESTIMATION

10648

15625

110592

The cube root of 10648 has to be calculated.

We will make groups of three digits starting from the rightmost digit of the number 10648, as $\overline{10} \overline{648}$. The groups are 10 and 648.

Considering the group 648,

648 ends with 8. We know that if the digit 8 is at the end of a perfect cube number, then its cube root will have its unit place digit as 2 only. Therefore, the unit place digit of the required cube root can be taken as 2.

Taking the other group i.e., 10,

We know that, $2^3 = 8 \mathrm{and} 3^3 = 27$

Also, 8 < 10 < 27

2 is smaller between 2 and 3. Therefore, 2 will be taken at the tens place of the required cube root.
Therefore; $\sqrt[3]{10648} = 22$
2) The cube root of 15625 has to be calculated.

We will make groups of three digits starting from the rightmost digit of the number 15625, as $\overline{15} \overline{625}$. The groups are 15 and 625.

Considering the group 625,

625 ends with 5. We know that if the digit 5 is at the end of a perfect cube number, then its cube root will have its unit place digit as 5 only. Therefore, the unit place digit of the required cube root can be taken as 5.

Taking the other group i.e., 15,

We know that, $2^3 = 8 \mathrm{and} 3^3 = 27$

Also, 8 < 15 < 27

2 is smaller between 2 and 3. Therefore, 2 will be taken at the tens place of the required cube root.
Therefore; $\sqrt[3]{15625} = 25$