Some Other Basic Math Operations
19
Ascertain with your calculator that (7.452)
2 = 55.53230; (3.71 x lO"
5 )
6 = 2.6076
x 1Q27
; (0.000429)
3
-
59 = 8.138 x 10~
13
; (6.405)"
3 = 3.086 x 10~
3
. Only positive
numbers normally can be raised to a power with the y
x key. If you try raising a
negative number to a power, you will get an error message in the display.
To find the power of a number by means of a log table, you use the logarithm
laws cited on page 14, as illustrated in the following problem.
PROBLEM:
Find the value of (2530)
5 .
SOLUTION:
Use the logarithm law for powers (log A" = n log A) to find the log of (2530)
5
; then
take the antilog to find the desired value.
log 2530 = log (2.53 x 10
3
) = log 2.53 + log !0
3
= 0.4031 + 3 = 3.4031
5 log 2530 = (5X3.4031) = 17.0155
(2530)
5 = antilog 17.0155 = 1.036 x 10
17
Roots
The root of a number is the result of raising that number to a power of less than
one. For simple cases we speak of the square root, cube root, fourth root, and
so on of a number (N), corresponding to TV*, TV*, TV*, and so on. In the general
case, the nth root of a number TV is simply TV"", where n may be any number
greater than one and is not limited to being an integer. Another common representation for these same roots is VTV, V/V, rfN. Any calculator will give the
square root directly. You just enter through the keyboard the number whose
square root you want, then press the Vx key, and the square root appears in the
lighted display.
For all other roots, it is simplest to use your calculator as follows, realizing
that the y
x key can just as well be used for y
lln where x = \/n.
1. Enter through the keyboard the number whose root you wish to take.
2. a. Press the ENTER key (on an HP-type calculator),
b. Press the y
x key (on a Tl-type calculator).
3. Enter through the keyboard the number (n) that corresponds to the
root you wish to take. This need not be an integer.
4. Press the reciprocal (l/x) key.
19
Ascertain with your calculator that (7.452)
2 = 55.53230; (3.71 x lO"
5 )
6 = 2.6076
x 1Q27
; (0.000429)
3
-
59 = 8.138 x 10~
13
; (6.405)"
3 = 3.086 x 10~
3
. Only positive
numbers normally can be raised to a power with the y
x key. If you try raising a
negative number to a power, you will get an error message in the display.
To find the power of a number by means of a log table, you use the logarithm
laws cited on page 14, as illustrated in the following problem.
PROBLEM:
Find the value of (2530)
5 .
SOLUTION:
Use the logarithm law for powers (log A" = n log A) to find the log of (2530)
5
; then
take the antilog to find the desired value.
log 2530 = log (2.53 x 10
3
) = log 2.53 + log !0
3
= 0.4031 + 3 = 3.4031
5 log 2530 = (5X3.4031) = 17.0155
(2530)
5 = antilog 17.0155 = 1.036 x 10
17
Roots
The root of a number is the result of raising that number to a power of less than
one. For simple cases we speak of the square root, cube root, fourth root, and
so on of a number (N), corresponding to TV*, TV*, TV*, and so on. In the general
case, the nth root of a number TV is simply TV"", where n may be any number
greater than one and is not limited to being an integer. Another common representation for these same roots is VTV, V/V, rfN. Any calculator will give the
square root directly. You just enter through the keyboard the number whose
square root you want, then press the Vx key, and the square root appears in the
lighted display.
For all other roots, it is simplest to use your calculator as follows, realizing
that the y
x key can just as well be used for y
lln where x = \/n.
1. Enter through the keyboard the number whose root you wish to take.
2. a. Press the ENTER key (on an HP-type calculator),
b. Press the y
x key (on a Tl-type calculator).
3. Enter through the keyboard the number (n) that corresponds to the
root you wish to take. This need not be an integer.
4. Press the reciprocal (l/x) key.