Question

find the square root of the following numbers using long devision method d) 100489​

Answer 1

Evaluation of square root of 100489 by long division method.

Procedure:

• Group the digits in the number into pairs (2 at a time) starting from the unit's place.

• Now take the largest number as a divisor and quotient whose square is less than or equal to the start pair.

• Now, like in every division method, subtract the resultant value from the above pair and bring the next pair to the right of the resultant of subtraction. This one acts as a new dividend.

• Now, to get the divisor to this iteration's new dividend, twice the previous divisor and annex it with a digit in such a way that the new divisor's (twiced number with annexed digit) product with the annexed digit is less than or equal to the new dividend. If so, just append the annexed number to the previous quotient.

• Repeat steps 3 and 4 till we get the remainder as 0.

Solution using long division method:

          3 |    10  04  89   |  317

               |    9                  |

      ----------------------------------------

       61    |      1   04         |

               |          61           |

      ----------------------------------------

      627  |           43  89     |

               |           43  89     |

      ----------------------------------------

                                   0

      ----------------------------------------

So, by long division method, the square root of 100489 is 317.

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