Page 23 - Schaum's Outline of Theory and Problems of Applied Physics

8 USEFUL MATH [CHAP. 1

SOLVED PROBLEM 1.18
Examples of square roots involving even exponents:
√
6
10 = 10 6/2 = 10 3
√
10 −4 = 10 −4/2 = 10 −2
√ √

4 4 2
5 × 10 = 5 × 10 = 2.24 × 10
√ √
−4
1.3 × 10 −8 = 1.3 × 10 −8 = 1.14 × 10
√ √
−1
9 × 10 −2 = 9 × 10 −2 = 3 × 10 = 0.3

SOLVED PROBLEM 1.19
Examples of square roots involving odd exponents:
√ √ √
5 5 4 4 2
10 = 1 × 10 = 10 × 10 = 10 × 10 = 3.16 × 10
√ √ √
10 −3 = 1 × 10 −3 = 10 × 10 −4 = 10 × 10 −4 = 3.16 × 10 −2
√ √

5 4 4 2
3 × 10 = 30 × 10 = 30 × 10 = 5.48 × 10
√ √
−4
6 × 10 −7 = 60 × 10 −8 = 60 × 10 −8 = 7.75 × 10
√ √ √ −3
0.000025 = 2.5 × 10 −5 = 25 × 10 −6 = 25 × 10 −6 = 5 × 10

SOLVED PROBLEM 1.20
Examples of cube roots:
√
3 9 9/3 3
10 = 10 = 10
√ √ √
3 8 3 2 6 3 3 6 2
10 = 10 × 10 = 100 × 10 = 4.64 × 10
√ √

3 19 3 18 3 3 18 6
3.8 × 10 = 38 × 10 = 38 × 10 = 3.36 × 10
√ √

3 −5 3 −6 3 3 −6 −2
2.7 × 10 = 27 × 10 = 27 × 10 = 3 × 10
UNITS

Units are algebraic quantities and may be multiplied and divided by one another. To convert a quantity expressed
in a certain unit to its equivalent in a different unit of the same kind, we use the fact that multiplying or dividing
anything by 1 does not affect its value. For instance, 12 in. = 1 ft, so 12 in./ft = 1, and we can convert a length
expressed in feet to its value in inches by multiplying it by 12 in./ft:

in.
4ft = (4 ft) 12 = 48 in.
ft
Conversion factors for the most common British and SI (metric) units are given in Appendix B.
Subdivisions and multiples of metric units are designated by prefixes that indicate an appropriate power
of 10. Standard prefixes are shown in Table 1.1.