B. Irrational Numbers and Radicals
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B. Irrational Numbers and Radicals
Irrational Numbers are related to radicals. In particular, square roots of non-perfect squares are Irrational Numbers.
Because Irrational Numbers cannot be expressed as fractions, and they do not terminate or repeat, it is often preferable to express them as exact values (radicals or
). They may also be represented in decimal form with three dots trailing the last written digit (
) or in approximated (rounded) decimal form (
).
It is also possible to estimate the value of an Irrational Number.
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Example 1 |
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Estimate the value of
Consider the closest perfect square smaller than 15 and the closest perfect square larger than 15. These two values will serve as
benchmarks to assist in estimating the value of
|
.
. Since the square roots of these perfect square values are
and
,
Using a calculator,
, which shows our estimate in
Example 1 to be quite accurate.
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Benchmark
a standard against which something can be compared or measured |