In the same way, if we wish to find √.148, or √.0148, or ✓.00148, or the square root of any number obtained by dividing 1.48 by any power of 10, we can get the answers from the column headed √n or V10 n by merely placing the decimal point properly. Thus, we find that V.148= .384708, √.0148=.121655, ✓.00148=.0384708, etc. What we have seen in regard to the square root of 1.48 or of that number multiplied or divided by any power of 10 holds true in a similar way for any number that occurs in the column headed n, so that the tables thus give us the square roots of a great many numbers. 2. Cube Roots. Cube roots are located in the tables in much the same way as that just described for square roots, but we have here three columns to select from instead of two, namely the columns headed Vn, V10 n, 100 n. Illustration. V1.48 occurs in the column headed Vn and is seen to be 1.13960. 14.8 occurs in the column headed V10 n and is seen to be 2.4552. V148 occurs in the column headed 100 n and is seen to be 5.28957. To get V.148 we observe that .148= 3/1.48 10 = 3 148 == 1 √148. 1000 10 The result is instantly .0148 we observe that 14.8. Thus, we look up V14.8 and divide it by 10, giving the result .24552. To get .00148 we observe that .00148=√√ that we must divide V1.48 by 10. This gives .11396. √1.48, so Similarly the cube root of any number occurring in the column headed n may be found, as well as the cube root of any number obtained by multiplying or dividing such a number by any power of 10. 3. Squares and Cubes. To find the square of 1.48 we naturally look at the proper level in the column headed n2. Here we find 2.1904, which is the answer. If we wished the square of 14.8 the result would be the same except that the decimal point must be moved two places to the right, giving 219.04 as the answer. Similarly the value of (148)2 is 21904.0 etc. On the other hand, the value of (.148)2 is found by moving the decimal place two places to the left, thus giving .021904. Similarly, (.0148)2.00021904, etc. To find (1.48)3 we look at the proper level in the column headed n3 where we find 3.24179. The value of (14.8)3 is the same except that we must move the decimal point three places to the right, giving 3241.79. Similarly, in finding (.148)3 we must move the decimal place three places to the left, giving .00324179. Further illustrations of the way to use the tables will be found in § 140. EXERCISES Read off from the tables the values of each of the following expressions. 1.14 1.15 1.16 1.17 1.3689 1.18 1.3924 1.19 1.4161 1.20 1.4400 1.21 1.22 1.23 1.09545 3.46410 1.4641 1.10000 3.47851 1.4884 1.10454 3.49285 1.5129 1.10905 3.50714 1.24 1.5376 1.25 1.5625 1.27 1.6129 1.12694 3.56371 1.28 1.6384 1.13137 3.57771 1.29 1.6641 1.13578 3.59166 1.30 1.6900 1.14018 1.31 1.7161 1.14455 3.61939 1.32 1.7424 1.14891 3.63318 1.33 1.7689 1.15326 3.64692 1.34 1.7956 1.15758 3.66060 1.35 1.8225 1.16190 3.67423 1.36 1.8496 1.16619 3.68782 1.8769 1.17047 3.70135 1.9044 1.17473 3.71484 1.9321 1.17898 3.72827 3.74166 2.74400 1.9881 1.18743 3.75500 2.80322 2.0164 1.19164 3.76829 2.86329 2.0449 1.19583 3.78153 2.92421 2.0736 1.20000 3.79473 2.98598 1.45 2.1025 1.20416 3.80789 3.04862 1.13185 1.46 2.1316 1.20830 3.82099 3.11214 1.13445 1.47 2.1609 1.21244 3.83406 3.17652 1.13703 2.44966 5.27763 1.48 2.1904 1.21655 3.84708 3.24179 1.13960 2.45520 5.28957 1.49 2.2201 1.22066 3.86005 3.30795 1.14216 2.46072 5.30146 1.2996 1.06771 3.37639 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.34164 4.24264 2.6896 1.28062 4.04969 2.7225 1.28452 4.06202 2.7556 1.28841 4.07431 4.57430 1.18405 2.7889 1.29228 4.08656 4.65746 1.18642 2.8224 1.29615 4.09878 4.74163 1.18878 2.56116 2.8561 1.30000 4.11096 4.82681 1.19114 2.56623 2.8900 1.30384 4.12311 2.9241 1.30767 4.13521 2.9584 1.31149 4.14729 2.9929 1.31529 4.15933 1.74 3.0276 1.31909 4.17133 1.75 3.0625 1.32288 4.18330 1.76 3.0976 1.32665 4.19524 1.77 3.1329 1.33041 4.20714 1.78 3.1684 1.33417 4.21900 1.79 3.2041 1.33791 4.23084 1.80 3.2400 4.41094 1.17927 2.54067 5.47370 4.49212 1.18167 1.34536 4.25441 5.92974 1.21869 2.62559 5.65665 1.34907 4.26615 6.02857 1.22093 2.63041 5.66705 1.35277 4.27785 6.12849 1.22316 2.63522 5.67741 1.84 1.85 1.86 3.3856 1.35647 4.28952 6.22950 1.22539 2.64001 3.4225 1.36015 4.30116 6.33162 1.22760 2.64479 3.4596 1.36382 4.31277 6.43486 1.22981 2.64954 5.70827 1.87 3.4969 1.36748 4.32435 6.53920 1.23201 2.65428 5.71848 1.88 3.5344 1.37113 4.33590 6.64467 1.23420 2.65901 5.72865 1.89 3.5721 1.37477 4.34741 6.75127 1.23639 2.66371 5.73879 1.90 3.6100 1.37840 4.35890 6.85900 1.23856 2.66840 5.74890 1.91 3.6481 1.38203 4.37035 6.96787 1.92 3.6864 1.38564 4.38178 7.07789 1.93 3.7249 1.38924 4.39318 7.18906 1.94 3.7636 1.39284 4.40454 7.30138 n n2 √n 2.00 4.0000 1.41421 2.01 2.02 4.0401 1.41774 2.03 4.1209 1.42478 2.04 2.08 2.09 10n 100 n 4.47214 8.00000 1.25992 2.71442 5.84804 4 48330 8.12060 1.26202 2.71893 5.85777 4.49444 8.24241 1.26411 2.72344 5.86746 4.50555 8.36543 1.26619 2.72792 5.87713 4.1616 1.42829 4.51664 8.48966 1.26827 2.73239 5.88677 2.05 4.2025 1.43178 4.52769 8.61512 1.27033 2.73685 5.89637 2.06 4.2436 1.43527 4.53872 8.74182 1.27240 2.74129 5.90594 2.07 4.2849 1.43875 4.54973 8.86974 4.3264 1.44222 4.56070 8.99891 4.3681 1.44568 4.57165 9.12933 √10n n3 | vn 1.27445 2.74572 5.91548 1.27650 2.75014 5.92499 11.6971 11.8524 12.0090 1.51658 4.79583 12.1670 12.3264 1.32192 2.84798 6.13579 12.4872 1.32382 2.85209 6.14463 12.6493 1.32572 2.85618 6.15345 1.31424 2.83145 6.10017 1.31809 2.83974 6.11803 1.32001 2.84387 6.12693 5.8564 1.55563 4.91935 14.1725 5.9049 1.55885 4.92950 14.3489 2.44 5.9536 1.56205 4.93964 14.5268 1.34626 2.45 6.0025 1.56525 4.94975 14.7061 1.34810 2.46 6.0516 1.56844 4.95984 14.8869 1.34993 2.47 6.1009 2.48 6.1504 2.49 6.2001 1.34072 2.88850 6.22308 1.34257 2.89249 6.23168 1.34442 2.89647 6.24025 2.90044 6.24880 2.90439 6.25732 2.90834 6.26583 15.0692 1.35176 2.91227 6.27431 15.2530 1.35358 2.91620 6.28276 2.92011 6.29119 |
