# What is the value of the cube root of 4913? Use an estimation method to find the cube root.

Answer

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Hint: Since this question is to find the cube root, make the group of digits in a group of 3 starting from right hand side as shown below

$\bar{4}\bar{913}$

Then apply concept finding the one’s digit of cube root if the number is given.

Number ending in 1 has a cube root ending in 1.

Number ending in 2 has a cube root ending in 8.

Number ending in 3 has a cube root ending in 7.

Number ending in 4 has a cube root ending in 4.

Number ending in 5 has a cube root ending in 5.

Number ending in 6 has a cube root ending in 6.

Number ending in 7 has a cube root ending in 3.

Number ending in 8 has a cube root ending in 2.

Number ending in 9 has a cube root ending in 9.

Number ending in 0 has a cube root ending in 0.

Then go on to the next group and search for the largest cube number smaller than the second group number.

We are given the number 4913.

Making a group of 3 digits starting from right we get,

$\bar{4}\bar{913}$

Now, one’s digit of cube root of 4913 is one’s digit of cube root of 913.

We know that any number which ends with 3 has a cube root ending in 7.

Applying this concept we concluded that one’s digit is 4913 is 7.

Now coming to the second group of numbers which is 4.

We search for the largest cube number which is less than the number in the second group.

Number in the second group is 4 and we know that

$\begin{align}

& 1\le 4<8 \\

& \Rightarrow {{1}^{3}}\le 4<{{2}^{3}} \\

\end{align}$

So the ten’s digit of cube root of 4913 is 1.

Hence the cube root of 4913 is 17.

Note: If the given number is more than 6 digits then this method changed a little bit. Actually only one group is made of 3 digits and the rest number on the left of the first group forms a second group. We have to search for the largest cube which is less than the number in the second group.

$\bar{4}\bar{913}$

Then apply concept finding the one’s digit of cube root if the number is given.

__Complete step-by-step answer:__Number ending in 1 has a cube root ending in 1.

Number ending in 2 has a cube root ending in 8.

Number ending in 3 has a cube root ending in 7.

Number ending in 4 has a cube root ending in 4.

Number ending in 5 has a cube root ending in 5.

Number ending in 6 has a cube root ending in 6.

Number ending in 7 has a cube root ending in 3.

Number ending in 8 has a cube root ending in 2.

Number ending in 9 has a cube root ending in 9.

Number ending in 0 has a cube root ending in 0.

Then go on to the next group and search for the largest cube number smaller than the second group number.

We are given the number 4913.

Making a group of 3 digits starting from right we get,

$\bar{4}\bar{913}$

Now, one’s digit of cube root of 4913 is one’s digit of cube root of 913.

We know that any number which ends with 3 has a cube root ending in 7.

Applying this concept we concluded that one’s digit is 4913 is 7.

Now coming to the second group of numbers which is 4.

We search for the largest cube number which is less than the number in the second group.

Number in the second group is 4 and we know that

$\begin{align}

& 1\le 4<8 \\

& \Rightarrow {{1}^{3}}\le 4<{{2}^{3}} \\

\end{align}$

So the ten’s digit of cube root of 4913 is 1.

Hence the cube root of 4913 is 17.

Note: If the given number is more than 6 digits then this method changed a little bit. Actually only one group is made of 3 digits and the rest number on the left of the first group forms a second group. We have to search for the largest cube which is less than the number in the second group.

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