FIND THE CUBE ROOTS BY ESTIMATION

10648

15625

110592

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; $\sqrt[3]{15625}=25$

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