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Numb. Square Roots Cube Roots.

Numb. Square Roots Cube Roots. Numb. Square Roots Cube Roots

1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512

1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561

38.2622
38.2753
38.2883
38.3014
38.3144
38.3275
38.3405
38.3536
38.3666
38.3796
38.3927
38.4057
38.4187
38.4317
38.4447
38.4577
38.4707
38.4837
38.4967
38.5097
38.5227
38.5356
38.5486
38.5616
38.5746
38.5875
98.6005
38.6134
38.6264
38.6393
38.6522
38.6652
38.6781
38.6910
38.7040
38.7169
38.7298
38.7427
38.7556
38.7685
38.7814
38.7943
38.8072
38.8200
38.8329
38.8458
38.8587
38.8715
38.8844

11.3548
11.3574
11.3599
11.3625
11.3651
11.3677
11.3703
11.3728
11.3754
11.3780
11.3806
11.3831
11.3857
11.3883
11.3909
11.3934
11.3960
11.3986
11.4011
11.4037
11.4062
11.4088
11.4114
11.4139
11.4165
11.4190
11.4216
11.4242
11.4267
11.4293
11.4318
11.4344
11.4369
11.4395
11.4420
11.4445
11.4471
11.4496
11.4522
11.4547
11.4573
11.4598
11.4623
11.4649
11.4674
11.4699
11.4725
11.4750
11.4775

38.8973
38.9101
38.9230
38.9358
38.9486
38.9615
38.9743
38.9871
39.0000
39.0128
39.0256
39.0384
39.0512
39.0640
39.0768
39.0896
39.1024
39.1152
39.1279
39.1407
39.1535
39.1663
39.1790
39.1918
39.2045
39.2173
39.2300
39.2428
39.2555
39.2683
39.2810
39.2937
39.3064
39.3192
39.3319
39.3446
39.3573
39.3700
39.3827
39.3954
39.4081
39.4208
39.4334
39.4461
39.4588
39.4715
39.4841
39.4968
39.5094

11.4801
11.4826
11.4851
11.4876
11.4902
11.4927
11.4952
11.4977
11.5003
11.5028
11.5053
11.5078
11.5103
11.5129
11.5154
11.5179
11.5204
11.5229
11.5254
11.5279
11.5304
11.5329
11.5354
11.5379
11.5404
11.5430
11.5455
11.5480
11.5505
11.5530
11.5554
11.5579
11.5604
11.5629
11.5654
11.5679
11.5704
11.5729
11.5754
11.5779
11.5804
11.5828
11.5853
11.5878
11.5903
11.5928
11.5953
11.5977
11.6002

E

Numb. Square Roots Cube Roots. Numb. Square Roots Cube Roots.

1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610

1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659

39.5221 39.5347 39.5474 39.5600 39.5727 39.5853 39.5979 39.6106 39.6232 39.6358 39.6484 39.6610 39.6736 39.6862 39.6988 39.7114 39.7240 39.7366 39.7492 39.7617 39.7743 39.7869 39.7994 39.8120 39.8246 39.8371 39.8497 39.8622 39.8748 39.8873 39.8998 39.9124 39.9249 39.9374 39.9499 39.9624 39.9749 39.9874 40.0000 40.0124 40.0249 40.0374 40.0499 40.0624 40.0749 40.0874 40.0998 40.1123 40.1248

11.6027 11.6052 11.6076 11.6101 11.6126 11.6151 11.6175 11.6200 11.6225 11.6249 11.6274 11.6299 11.6323 11.6348 11.6372 11.6397 11.6422 11.6446 11.6471 11.6495 11.6520 11.6544 11.6569 11.6594 11.6618 11.6643 11.6667 11.6692 11.6716 11.6740 11.6765 11.6789 11.6814 11.6838 11.6863 11.6887 11.6911 11.6936 11.6960 11.6985 11.7009 11.7033 11.7058 11.7082 11.7106 11.7131 11.7155 11.7179 11.7203

40.1372 40.1497 40.1621 40.1746 40.1870 40.1995 40.2119 40.2243 40.2367 40.2492 40.2616 40.2740 40.2864 40.2988 40.3112 40.3236 40.3360 40.3484 40.3608 40.3732 40.3856 40.3980 40.4103 40.4227 40.4351 40.4474 40,4598 40.4722 40.4845 40,4969 40.5092 40.5215 40.5339 40.5462 40.5585 40.5709 40.5832 40.5955 40,6078 40.6201 40.6324 40.6448 40.6571 40.6693 40.6816 40.6939 40.7062 40.7185 40.7308

11.7228 11.7252 11.7276 11.7300 11.7325 11.7349 11.7373 11.7397 11.7421 11.7446 11.7470 11.7494 11.7518 11.7542 11.7566 11.7590 11.7614 11.7639 11.7663 11.7687 11.7711 11.7735 11.7759 11.7783 11.7807 11.7831 11.7855 11.7879 11.7903 11.7927 11.7951 11.7975 11.7999 11.8023 11.8047 11.8071 11.8094 11.8118 11.8142 11.8166 11.8190 11.8214 11.8238 11.8261 11.8285 11.8309 11.8333 11.8357 11.8381

Numb. Square Roots Cube Roots.

1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694

40.7430
40.7553
40.7676
40.7798
40.7921
40.8044
40.8166
40.8289
40.8411
40.8533
40.8656
40.8778
40.8900
40.9023
40.9145
40.9267
40.9389
40.9511
40.9633
40.9756
40.9878
41.0000
41.0121
41.0243
41.0365
41.0487
41.0609
41.0731
41.0852
41.0974
41.1096
41.1217
41.1339
41.1460
41.1582

11.8404
11.8428
11.8452
11.8476
11.8499
11.8523
11.8547
11.8571
11.8594
11.8618
11.8642
11.8665
11.8689
11.8713
11.8736
11.8760
11.8784
11.8807
11.8831
11.8854
11.8878
11.8902
11.8925
11.8949
11.8972
11.8996
11.9019
11.9043
11.9066
11.9090
11.9113
11.9137
11.9160
11.9184
11.9207

1695 41.1703
1696 41.1825
1697 41.1946
1698 41.2067
1699 41.2189
1700 41.2310
1701 41.2431
1702 41.2553
1703 41.2674
1704 41.2795
1705 41.2916
1706

41.3037
1707 41.3158
1708 41.3279
1709 41.3400
1710 41.3521
1711 41.3642
1712 41.3763
1713 41.3884
1714 41.4004
1715 41.4125
1716 41.4246
1717 41.4366
1718 41.4487
1719 41.4608
1720 41.4728
1721 41.4849
1722 41.4969
1723 41.5090
1724'' 41.5210
1725 41.5331
1726 41.5451
1727 41.5571
1728 41.5692

11.9231
11.9254
11.9278
11.9301
11.9324
11.9348
11.9371
11.9395
11.9418
11.9441
11.9465
11.9488
11.9511
11.9535
11.9558
11.9581
11.9605
11.9628
11.9651
11.9675
11.9698
11.9721
11.9744
11.9768
11.9791
11.9814
11.9837
11.9860
11.9884
11.9907
11.9930
11.9953
11.9976
12.0000

To find the Root of a Number, consisting of Integers

and Decimals. Rule.—Multiply the difference between the root of the integer part of the given number, and the root of the next higher integer number, by the decimal part of the given number, and add the product to the root of the integer number given; the sum will be the root of the number required, correct in all cases of the square root to 3 places of decimals, and in the cube root to 7.

EXAMPLE 1.—Required the square root of 60.2.

161
160

7.8102
7.7459

[blocks in formation]

V 60.2 7.75876 as required, correct to

3 places of decimals. EXAMPLE 2.-Required the cube root of 843.75.

3/844 = 9.4503 3843 - 9.4466 difference .0037 Х

.75

[blocks in formation]

If the square root is required correct to more places of decimals, the following rule is correct to 7 places.

Multiply the root of the nearest integer number by twice the difference between that and the given number, and divide the product by 3 times the integer number added to the given number; and the quotient added to the root of the integer number will be the root of the given number nearly. Then, the root of 60.2 will stand thus,

760 7.7459

Х .4 2x2 60x3 180+60.2 - 240.2)3.09836(.01289+7.7459 7.75889 the

2402

[root required. 6963 4804

21596
19216

23800

If the number consist wholly of decimals, the root will be decimals also.

PRACTICAL GEOMETRY.

Practical Geòmetry is the art of describing mathematical figures by a ruler and compasses, or other instruments proper for the purpose.

PROBLEM I.

To divide a given Line into two equal parts.

From A and B as centres, with any distance greater than half the length of the line, describe arcs cutting each other in m and n; then a line drawn through the points m and n will divide the line into two equal parts, as required.

A

-B

im

PROBLEM II.

To divide a given Angle into two equal parts.

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From the point C as a centre, with any distance at pleasure, describe the arc A B; and from A and B as centres, with the same or any other convenient distance, describe arcs cutting each other in n; then a line drawn from the point C, through n, will divide the angle as required.

B

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