ORAL DRILL 1. Find from the above table the sum to which $1 will amount in ten years at 4%. 2. To what will $ 1 amount in seven years at 6% ? 1 4 9 16 25 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 49 64 81 100 121 144 169 196 225 256 289 324 361 400 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 1.0000 1.0000 3.142 0.7854 1.4142 1.2599 6.283 3.1416 1.7321 1.4422 9.425 7.0686 2.0000 1.5874 12.566 12.5664 2.2361 1.7100 15.708 19.6350 2.4495 1.8171 18.850 28.2743 2.6458 1.9129 21.991 38.4845 2.8284 2.0000 25.133 50.2655 3.0000 2.0801 28.274 63.6173 3.1623 2.1544 31.416 78.5398 3.3166 2.2240 34.558 95.0332 3.4641 2.2894 37.699 113.0973 3.6056 40.841 132.7323 3.7417 2.4101 43.982 153.9380 3.8730 2.4662 47.124 176.7146 4.0000 2.5198 50.265 201.0619 4.1231 2.5713 53.407 226.9801 4.2426 2.6207 | 56.549 254.4690 4.3589 2.6684 59.690 283.5287 4.4721 2.7144 62.832 314.1593 2.35134 15 16 17 18 19 20 7. To what will $ 10 amount in 10 years at 7 %? 8. To what will $ 100 amount in 7 years at 6 % ? 9. To what will $ 1000 amount in 12 years at 7 %? 10. To what will $1000 amount in 20 years at 51 % ? ORAL DRILL 1. Find from the table the square of 18. 7. What is the circumference of a circle whose diameter is 3 ? 8. What is the area of a circle whose diameter is 14 ? 9. What is the circumference of a circle whose diameter is 15 ? 10. What is the area of a circle whose diameter is 20 ? CHAPTER VIII SQUARE ROOT AND CUBE ROOT Square Root The square root of a number is one of the two equal numbers which multiplied together will produce the number. Thus, 7 is the square root of 49, and is the square root of 3: The square root of a number is usually indicated by writing the number under the radical signy. The expression V81 is. read “ the square root of 81.” The square root of a fraction is found by taking the square root of the numerator and of the denominator. Thus, the square root of 1 is . Since 1= 12, 100 = 102, 10,000 = 1002, and so on, the square root of a number between 1 and 100 lies between 1 and 10; of a number between 100 and 10,000, lies between 10 and 100. In other words, the square root of a number expressed by one or two figures is a number of one figure ; of a number expressed by three or four figures is a number of two figures; and so on. If therefore a number is divided into groups of two figures each, from right to left, the number of figures in its square root will be equal to the number of groups of figures. The last group to the left may consist of one figure or of two figures. ORAL DRILL 25.4 26. 25 27. 2 5 What are the square roots of the following numbers ? 17. 400 18. 441 19. 625 20. 10,000 13. 196 14. 256 23. 36 16. 289 28.1 21. 1 22. L'e 29.24 30. 2 5 31. 49 24. 196 64 81 202 = EXAMPLE 1. Find the square root of 625. 6 25 20 or, more briefly, 4 00 6 25 25 2 x 20 = 40 2 25 5 4 5 2 25 25 45 2 25 45 2 25 1100 Since 625 consists of two groups of figures, its square root is composed of two figures, tens and units. Since the square of tens is hundreds, 6 hundreds must be the square of at least 2 tens. Two :20 tens or 20 squared is 400, as shown in figure A ; and 625 400 leaves a remainder of 225. The root 20, therefore, must be 20 so increased as to use up the re mainder and keep the figure a 20 square. A The necessary additions to A to keep it a square are the two rectangles B and C, and the small square D. B, C, and D contain 225 square units. Since the area of D is small, if 225 is divided by 40, the combined length of B and C, the quotient will indicate the approximate width of these additions. The quotient is 5; the entire length of B, C, and D is 20 + 20+ 5=45 units; and the B В area of the additions is 5 times 45, or 225 square units. Since these three additions use up the re 20 maining 225 square units and keep the figure a square, the side of the required square is 25 units, and the square root 20 of 625 is 25. In extracting square root arithmetically the following is a convenient rule. Rule. — (1) Beginning at the units' place, separate the number into groups of two figures each. (2) Find the largest square in the first group on the left and write its su root as the first figure in the answer. (3) Subtract its square from the group and annex the second group to the remainder. (4) For a trial divisor use twice the part of the root already found. Divide the remainder, omitting the last figure, by this trial divisor, and annex the quotient to the root and also to the trial divisor. (5) Multiply the complete divisor by the second figure of the root and subtract the product from the remainder. (6) Double the part of the root already found, for another trial divisor, and proceed as before. (7) Continue this process until all of the groups have been used. NOTE. When a zero occurs in the root, annex a zero to the trial divisor, bring down another group, and proceed as before. |