When there are more figures in the dividend, bring down each successive period, and proceed as before. 2. What is the square root of 256? 5. Extract the square root of 5625. ANS. 75. ANS. 325. ANS. 462. 7. What is the square root of 213444? ANS. 652. ANS. 987. ANs. 3275. ANS. 4632. SECTION IV. Square Root of Fractions. Change the fractions to their highest denominators, then extract the square root of the numerator, and the square root of the denominator, and they will express the square root of the fraction. 1. 2. 3. What is the square root of 경우? ANS. 글공=글· 5625 ANS. . What is the square root of 22. ANS. 13. SECTION V. Extraction of the Cube Root. To extract the cube root of any given number. Separate the number by pointing off successively three figures beginning at the right. 1. What is the cube root of 42875? 42.875 From the left hand period subtract the greatest cube it contains, and place its root in the quotient. 42.875 (3 27 15 The greatest cube in 42 is 27, the root of which is 3. Bring down the first figure of the next period and place it at the right of the remainder for a new dividend. Multiply the square of the quotient by 3, for a new divisor; and in the quotient write the number of times it is contained in the dividend. Subtract the cube of the quotient from the first two periods of the dividend. The cube of 35 is 42875, there will then be no remainder; and as there are no more figures in the dividend the work is completed, and 35 is the cube root required. 2. What is the cube root of 12812904? Change the fraction to its highest denominator, then extract the root of its numerator, and the root of its denomnator, and they will express the cube root of the fraction. 1. What is the cube root of 27? The cube root of 27 is 3, and the cube root of 125 is 5. 2. What is the cube root of 43 ANS. . ANS. . 3. Extract the cube root of 54 tor. 432. This fraction may be changed to a higher denomina54 divided by 2 is 27; the cube root of 27 is 3. 432 divided by 2 is 216; the cube root of 216 is 6. ANS. SECTION VII. Proportionals. A. To find a mean proportional between two numbers. Multiply the two numbers together, and the square root of the product is the proportional required. 1. What is the mean proportional between 8 and 18? 188=144, the square root of which is 12. ANS. 12. 2. What is the mean proportional between 12 and 27? ANS. 18. 3. What is the mean proportional between 27 and 75 ? ANS. 45. 4. Find the mean proportional between 71 and 30. ANS. 15. 5. Find the mean proportional between 64 and 100. ANS. 80. 6. What is the mean proportional between 72 and 128 ? ANS. 96. 7. What is the mean proportional between 135 and 375? ANS. 225. B. To find a proportional to the less of two numbers, Divide the square of the less, by the greater number, the quotient will be the proportional required. 1. What is the less proportional to 12 and 18? 12 × 12=144 188 the less proportional. 2. What is the less proportional to 36 and 54 ? ANS. 24. 3. What number bears the same proportion to 40, that 40 bears to 64? ANS. 25. the C. To find a proportional to the greater of two numbers. Divide the square of the greater by the less number, quotient will be the proportional required. 1. What is the proportional greater to 9 and 15? 15 X 15=2259-25 the greater proportional. What is the proportional to the greater of 12 and 2. 18? ANS. 27. 3. What number bears the same proportion to 40 which 40 bears to 25 ? ANS. 64. D. To find a fourth proportional to the least in a series of three numbers. Divide the product of the first two by the last number, the quotient will be the proportional. 1. What is the fourth less proportional to 5, 8, and 5X84012-31. 12? 2. 27! Ans. 3. What is the fourth less proportional to 9, 18 and ANS. 6. 3. What number is in the same proportion to 12 which 27 is to 36? ANS. 9. E. To find a fourth proportional to the greatest in a series of three numbers. Divide the product of the last two by the first number, the quotient will be the proportional required. |