Mental Math: SQRT(499849) =______

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to create groups of two, starting from right to the left such that:

`sqrt((49)(98)(49))`

You need to find a number whose square yields 49 and this number is 7.

You need to square 7 and you need to write 49 under the first group 49 and then you need to perform the subtraction such that:

`sqrt((49)(98)(49))`

      - 49

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

         //

You need to bring down the next group and you need to double 7 such that:

`sqrt((49)(98)(49)) ` | 7

      - 49                __________

-----------------     14

        //    98

You need to put a digit next to 14 such that 14 multiplied by what other number yields 98, hence, you should put 0. 

`sqrt((49)(98)(49))`  | 70

      - 49               __________

-----------------     140 x 0 = 0

         // 98       ____________

               0            1407 x 7 = 9849

 _________________

                9849

                9849

You out 0 next to 7 and then you need to double 70. Then, you need to find what digit must complete the number 140 such that `140a*a = 9849` .

Hence, evaluating the square root of the given number yields `sqrt(499849) = 707` .

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