In
mathematics, it is sometimes important for us to
be able to estimate the values of square roots
(radicals). This is especially the case on exams
that do not allow the use of a calculator, and you
try to eliminate wrong answers, or verify the
reasonableness of your response. Also in the
geometry, the values sqrt(2) and SQRT(3) come up so
often that it is important to know their approximate
values.
This article shows you the steps to estimate a
square root. The article assumes that you have a
basic understanding of square roots and perfect
squares. See the
Reference for more information.
1. In order to assess the value of the square root
of a number, find the perfect squares are above and
below the number. For example, to estimate the sqrt
(6), note that 6 is between the perfect squares 4
and 9. SQRT (4) = 2, and sqrt (9) = 3. Since 6 is
closer to 4 than it is to 9, we'd expect its square
root to be closer to 2 than it is to 3. It is
actually about 2.4, but as long as you knew, it was
in this ballpark, you'd be fine. Even just to know
that it was somewhere between 2 and 3 would be to
your advantage.
2. Let's try another example. Assessment sqrt (53).
53 is between the perfect squares 49 and 64, the
square roots, which are 7 and 8, respectively. 53 is
closer to 49 than at 64, so it would be reasonable
to estimate the sqrt (53) to be between 7 and 7.5.
It turns out that it is around 7.3.
3. There are two square roots that come up very
often in geometry. They are sqrt(2) and SQRT(3). It
is very important that you remember their
approximate values. Note that sqrt (1) is 1, and
sqrt (4) is 2. . Based on this, it should come as no
surprise that sqrt(2) is approximately 1.4, and
SQRT(3) is approximately 1.7. The most important
thing is to remember that sqrt(2) is greater than 1,
and sqrt (3) is less than 2. another article
discusses the application of these square roots in
working with right triangles and the Pythagorean
theorem.
4. Students should ensure that they are comfortable
with estimating square roots, and for that matter
estimating all your answers to see if they are
reasonable. This will usually allow you to catch
your mistakes before you hand in your exams. |