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THE NEW  STUDENT'S   REFERENCE  WORK

2207

B

Find the square root of 1225. A 1&            The first period, 12, contains the square of the tens' figure

_9__        of the root.

65  325                The greatest square in 12 is 9. Write the square root of 9,

325        which is 3, as the tens' figure of the root. Subtract the square

of the tens' figure, and the remainder, together with the next period, contains twice the tens' figure X the unit + the unit 2. Twice the 3 tens is 6 tens, and 6 tens are contained in 32 tens of the remainder, 5 times. The 5 is the units figure of the root, and to save one multiplication we also add the units figure to the right of the 6 tens in the divisor. The 65 is called the complete divisor. Multiply the complete divisor and subtract. There is no remainder.

The square root of 1225 is 35.

Find the square of 46.

Start with a square 40 units wide (Figure A). What is its length!

Increase the dimensions of the square 6 units. How long will the square be ? How wide ? Note that the areas added are 2 equal rectangles, each as long as a dimension of the original square, and a small square, whose dimensions will be the width of one of the rectangles (Figure B).

402 = 1600 area of original square. (40 X 6) 2 = 480 area of two rectangles.

62 =    36 area of small square. 462 = 2116 area of enlarged square.

Find the square root of 2116.

-£r i\               The first period, 21, contains area of the original square,

16             1600.    Subtracting this area, we have the remainder, 516.

86 | 516                516 contains the area of the two equal rectangles and

516         the area of the small square.

We wish to find the width of the rectangles.

The length of the rectangles is 80 units, or twice the tens' figure in the root. This is our trial divisor. Divide the area of these rectangles by their length and we get 6, the width of the rectangle, or the units' figure in the root. Add this units' figure to the trial divisor, which gives the length of the twro rectangles + the length of the small square. This is the complete divisor, 86. Multiply the length by the width and it gives 516 square units; subtract and nothing remains.

The square root of 2116 is 46.