solution of square root of 30349081

Question

it is one kind of division square root question.

Answer 1

Answer 5509.

 30 | 34 | 90 | 81 Split into pairs.

Closest square to 30 which is less than 30, is 25=5², so first digit of solution is 5:

   5

 30 | 34 | 90 | 81

-25

    534

Create "divisor"=20×5+r=100+r. Guess r so that r(100+r) is as close as possible to 534 without exceeding it. Guess 5 because 5×105=525. 6 would be too big (6×105=630).

          5     5     0     9

        30 | 34 | 90 | 81

       -25

105 |  534                   (r(2×5×10+r) ≤ 534, so r=5, 5×105=525, 5 is next digit)

           -525

 1100 |    990              (r(2×55×10+r) ≤ 990, so r=0, 0 is next digit)

 11009 |  99081          (r(2×550×10+r) ≤ 99081, so r=9, 9×11009=99081, 9 is last digit)

                -99081

                    0