The Mathematics 11
Competency Test
Determination of Roots Using a
Calculator
All scientific calculators have a built-in function labelled
numbers. On many, you must press the 2
key.
To check that you are using the
nd
for calculating square roots of
Function or INV key first, before pressing the
key correctly, try duplicating the following three examples:
2 = 1.414213562
3 = 1.732050808
843.17 = 29.03738969
You may have more or fewer digits in the display on your calculator, but your results should agree
with those above for the first six or seven digits from the left.
A few of the more advanced calculators have cube root keys which work in the same way as the
key. However, it is unlikely that your calculator will have keys for any higher order roots. To
calculate cube roots (if your calculator doesn’t have a
n
x =x
That is, the 1
n
1
n
3
key) or a higher order root, recall that
.
power is the same as the nth root of a number. All scientific calculators have
power or exponentiation keys, often labelled xy or yx or ab, etc. Thus, for example,
3
17 = 17
1
3
≅ 2.571281591
rounded to nine decimal places. You need to be careful to get the exponent 1
3
entered as
accurately as possible. If you approximate 1 ≅ 0.33 you will get
3
3
17 = 17
1
3
≅ 170.33 = 2.547112599
a result which is already wrong in the second decimal place. This is probably too rough for many
applications.
Perhaps the easiest way to get the highest accuracy that your calculator can achieve is to enter
fractions such as 1
3
exactly in this form, without first converting them to decimal numbers. The
keystrokes required in this example would be something like:
David W. Sabo (2003)
Roots by Calculator
Page 1 of 2
1
yx
7
(
1
÷
3
)
=
Here are a few more examples for you to practice with:
3
487.3 = 487.3
4
1486 = 1486
7
67 = 67
David W. Sabo (2003)
1
7
1
4
1
3
≅ 7.869228155
≅ 6.208757568
≅ 1.823340711
Roots by Calculator
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