We know it is a 3 digit root. The last digit must end in 7, because the last digit of 7^3 is 3. The first digit is obviously 9. So now just guess the second digit. Start with 997^3. And that is the answer
For those who want to calculate cube root of any number with paper and pencil method (10a+b)^3=1000a^3+300a^2b+30ab^2+b^3 (10a+b)^3 - 1000a^3 = 300a^2b+30ab^2+b^3 (10a+b)^3 - 1000a^3 = (300a^2+30ab+b^2)b (10a+b)^3 - 1000a^3 = ((300a^2+b^2)+30ab)b How number on the side is constructed We triple the square of current approximation and append to it square of last digit of next approximation Then we add to this number triple of current approximation and last digit of next approximation but shifted one position to the left Finally we multiply it by last digit of next approximation To estimate last digit of next approximation division may be helpful
We know it is a 3 digit root.
The last digit must end in 7, because the last digit of 7^3 is 3.
The first digit is obviously 9.
So now just guess the second digit. Start with 997^3. And that is the answer
For those who want to calculate cube root of any number with paper and pencil method
(10a+b)^3=1000a^3+300a^2b+30ab^2+b^3
(10a+b)^3 - 1000a^3 = 300a^2b+30ab^2+b^3
(10a+b)^3 - 1000a^3 = (300a^2+30ab+b^2)b
(10a+b)^3 - 1000a^3 = ((300a^2+b^2)+30ab)b
How number on the side is constructed
We triple the square of current approximation and append to it square of last digit of next approximation
Then we add to this number triple of current approximation and last digit of next approximation but shifted one position to the left
Finally we multiply it by last digit of next approximation
To estimate last digit of next approximation division may be helpful
Thanks for well calculated solution.🥰
The answer is 997. Now I am going to compare that to another problem incolvinf fifth roots.