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2538. A man buys a farm of 160 acres which he rents for a period of 3 years for $4 an acre per year. How much does the rent amount to?

2539. He pays a premium of 1| % annually to keep the house and barn insured for $800. What does he pay out for insurance?

2540. The land is assessed at f 20 per acre, and the rate of taxation the-first two years is 15 mills on the dollar. The next year, 17 mills on the dollar. Find the amount of his taxes for three years.

2541. During the three years, he puts on the place improvements amounting to $108.80. How much more than the expenses is the rent?

2542. What is his average yearly per cent of profit?

2543. How much will a debt of $200 amount to in 2 yr. 3 mo. 5 da. at 6% interest?

2544. If the law firm of Lowe and Son charges 6 % for making collections, how much should it receive for collecting a note of $1500, dated Oct. 10, 1900, at i\% interest, if the collection is made June 7, 1902?

2545. $350. Chicago, Iii., Aug. 3, 1904. One year after date I promise to pay to the order

of John H. Fisher, Three Hundred and Fifty Dollars, without interest if paid when due. If not paid when due to draw interest from date at 6%, for value received.

H. W. Mayes.

Find the amount of this note if paid Apr. 10, 1905.

2546. Write a note which does not draw interest when due, otherwise to draw 5% interest from date. Find the amount of this note if paid 6 months after maturity.

2547. Make an interest-bearing note, dated May 4,1902, face of the note $610, time to run 1 year, rate 6%, payee R. O. Gilbert.

2548. If this note is settled June 6, 1904, compute the amount due at settlement.

2549. Make a note, payable on demand, face of note $2500, James Meeks payee, drawing 5% interest, dated Mar. 1, 1903.

2550. Compute the amount of this note, if it is settled Sept. 7, 1904.

2551. Make a note of $300 for 60 days, drawing 7% interest, with W. F. Pierce as payee.

2552. What will be the amount if settled 1 yr. 3 mo. after date?

2553. A man borrows $25,000 at 5|% interest and loans it immediately at 7|%. What does he gain in 9 months?

2554. When the interest on $234.25 is $35.2875 for

2 yr. 6 mo., what is the rate?

2555. When $350 amounts to $368.35 in 1 yr. 9 mo. 18 da., what is the rate?

2556. Find the time in which $238.75 will yield $128.92 interest at 9%.

2557. Find the sum that will yield $52.50 interest in

3 yr. 6 mo. at 5%.

CHAPTER IX

ROOTS

2558. What are the prime factors of 1600? Group these factors so as to find the two equal factors of 1600. In like manner find the two equal factors of 2500; of 2304. What are the equal factors of a number called?

2559. Find the second root of 169; of 441; of 1296; of 1225.

2560. Find the second power of 12; of 18; of 25; of 300; of 53.

Note. The power of a number is indicated by a small figure placed to the right and above the number, thus,

52 = 5 x 5=25. 63 = 6 x 6 x 6 = 216.
4B = 4 x4 x4x 4 x4= 1024.

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Note. In finding the square root of larger numbers another method is employed. The number is divided into periods of two places each from the decimal point. Find the greatest square in the period to the left, and find its root. Subtract the square from the number and bring down the next period. Proceed in this manner as illustrated in the problems below.

2565. Find the square root of 576.

Solution

The largest square in 576 is 400. The remaining portion, 176, is made up of two rectangles, each the length of the square found, 20, and a square whose dimensions equal the width of these rectangles. Placing the rectangle X in the position Y, we see that the three remaining figures together form a rectangle, and that it is more than 40 units long. Dividing this area, 176, by 40, we see that the width of the rectangle is 4, or nearly 4. Adding this 4 to the incomplete divisor, 40, we have the complete divisor, 44. Multiplying 44, which represents the entire length of the rectangle, by 4, which represents the width of the rectangle, we have the area 176. Subtracting this product from the original square, nothing remains. Therefore the square root of 576 is 24.

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2566. Find the square root of 7396. What is the length of the square whose area is 6400? What is the length of the two rectangles? Why is 6 added to 160? What is the length of the two rectangles and the small square?

2567. Find the square root of 1440.

2568. Find the square root of 625, 2500, 8649, 3721, 324.

2569. Find the square root of 441, 1296, 2401, 6561, 7744.

2570. Find the square root of 55,225.

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The largest square in the first period of this number is 40,000. One side of this square is 200. The length of the two rectangles is 430. To find the width of the two rectangles and the square adjoining, we divide the area of the three figures, 15,225, by the length of the two rectangles, 400. The quotient is 30, nearly. The length of the two rectangles and the square together is 430. Multiplying this by 30, the width, and subtracting the product, the remainder is 2325.

Each of the two remaining rectangles is 230 units long. Dividing 2325 by 460, the quotient is 5, their width. Adding 5, a side of the square, to the length of the two rectangles, and multiplying by 5, the product is 2325. Nothing remains. The square root of 55,225 is 235.

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