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Friday, October 7, 2016

Cube root Part 2

Arithmetic


  1. Looking at the two procedures to find the cube root of two and three digit numbers in previous post (Cube roots Part 1). We can follow the following procedure to find the cube root of any number. This method is called the division method.

    1. Group the digits from right into triples. If the number has a decimal part, make triples to both sides of decimal. If the decimal part has one or two digit left, add one or two zero correspondingly to it.

    2. Find  a number whose  cube is less than or equal to the first triple or the remaining digits after forming triple. Take it as divisor and quotient.

    3. Subtract the cube of divisor  from the first triple or the remaining digits after forming triples.

    4. Bring down the next triple to the right of the remainder. This is the new dividend.

    5. Take the thrice of quotient below on the left column of the new dividend.

    6. The new divisor is obtained by annexing the thrice of the quotient by a digit. The digit is such that [(10×(the thrice of quotient)×(quotient annexed  by new digit)×(new digit)) + (new digit)3] is less than or equal to the new dividend.

    7. Annex the new digit to the top quotient.

    8. Subtract the number obtained by [(10×(the thrice of quotient)×(quotient annexed  by new digit)×(new digit)) + (new digit)3]  from the dividend.

    9. Repeat the process.

    10. In case of taking quotient to decimal, add zeros to right of remainder in triples.

    11. Cube root of 15625 is 25.

      cube root of 15625


    12. Cube root of 2352637

      cube root of 2352637



    13. Cube root of 2352.637

      cube root of 2352.637



    14. Cube root of 2.352637

      cube root of 2.352637



    15. Cube root of 2 is 1.259...
      cube root of 2




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