Question
Find the cube root of 614125 through estimation.
✓
Answer
Given, number is 614125.
So, groups of 614125 are
In the first group, the number 125 ends with 5.
We know that 5 comes at the unit place of a number only when its cube end in 5.
So, 5 will come at unit place.
Now, in the second group, the number is 614.
$\begin{array}{l}\because(8)^3=512 \text { and }(9)^3=729 \\ \text { and } 512<614<729\end{array}$
So, tens place of required cube root is 8.
Hence, $\sqrt[3]{614125}=85$
So, groups of 614125 are
In the first group, the number 125 ends with 5.
We know that 5 comes at the unit place of a number only when its cube end in 5.
So, 5 will come at unit place.
Now, in the second group, the number is 614.
$\begin{array}{l}\because(8)^3=512 \text { and }(9)^3=729 \\ \text { and } 512<614<729\end{array}$
So, tens place of required cube root is 8.
Hence, $\sqrt[3]{614125}=85$
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