Question

you are told that 1331 is a perfect cube.can you guess without factorization what is its cube root?similarly guess the cube root of 4913,12167,32768.with full formula (only number)​

Answer 1

Answer

1331=we divide 1331 into groups of three digits starting from the right. So 1331 has two groups one is 331 and another is 1.

For first group 331, the digit 1 is at one's place .1 comes at a unit place of a number only when its cube root ends with 1. So one's place of the required cube root is 1.

For another group, i.e.1 1

3

=1 and 2

3

=8 so 1 lies between 0 and 8.the smaller number among 1 and 2 are 1. So the one's place of 1 is 1 and ten's place of cube root 1331 is 1

Hence

3

1331

=11

For 4913

we divide 4913 into groups of three-digit starting from the right. So 4913 has two groups one is 913 and another is 4.

For first group 913, the digit 3 is at one's place .3 comes at a unit place of a number only when its cube root ends in 7. So one's place of the required cube root is 7.

For another group, i.e.1 1

3

=1 and 2

3

=8 so 4 lies between 1 and 8.the smaller number among 1 and 2 are 1. So the one's place of 1 is 1 and ten's place of cube root 4913 is 1

Hence

3

4913

=17

For 12167

we divide 12167 into groups of three-digit starting from the right. So 12167 has two groups one is 167 and another is 12.

For first group 167, the digit 7 is at one's place .7 comes at a unit place of a number only when its cube root ends in 3. So one's place of the required cube root is 3

For another group, i.e.12 2

3

=8 and 3

3

=27 so 12 lies between 8 and 27.the smaller number among 2 and 3 are 2. So the one's place of 2 is 2itself and ten's place of cube root 12167 is 2

Hence

3

12167

=23

For 32768

we divide 32768 into groups of three-digit starting from the right. So 32768 has two groups one is 768 and another is 32.

For first group 768, the digit 8 is at one's place .8 comes at the unit place of a number only when its cube root ends in 2. So one's place of the required cube root is 2.

For another group, i.e.1 3

3

=27 and 4

3

=64 so 32 lies between 27 and 64.the smaller number among 3 and 4 are 4.So the ten's place of cube roo

32768

=32