Question

find the cube root of the following cube numbers through estimation. 1>4913. 2>103823. 3>205379. 4>12167

Answer 1

Answer:

For calculating the cube root of 4913, this has to be separated in to 3 groups starting from rightmost digit.

The group are 4 and 913.

Considering the group 913

913 ends with 3 and we know that if the digit 3 is at the end of any perfect cube number, then it's cube root will have 7 at its units place only. Therefore the digit at units place of the required cube root is taken as 7.

Now considering the other group 4

We know that 1^3=1 and 2^3=8

Also, 1<4<8

So, 1 will be taken at the tens place. so the required cube root of 4913 is 17.

So, final answer is 17.

Apply same procedure to next two numbers:

2) 12167

The groups are 12 and 167

167 ends with 7 and we know that if 7 is at the unit place of any perfect cube number then it's cube root will have 3 at its units place only. the digit at the units place of required cube root is taken as 3.

Now group 12,

2^3=8 and 3^3=27 also 8<12<27

2 is smaller than 3, therefore 2 is taken as the digit at tens place of the required cube root.

Thus, cube root of 12167 is 23.

3) 32768

The groups are 32 and 768

768 ends with 8.

8 at the unit place of perfect cube number, then it's cube root will have 2 at its units place only. So, the digit at the units place of required cube root is 2.

Now group 32,

3^3=27 and 4^3=64 also 27<32<64

3 is smaller than 4, therefore 3 is taken as the digit at tens place of the required cube root.

Thus, cube root of 32768 is 32.

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Hope you understand.