Unit 3 sec 3.3
Surds
12 November 2015
23:15
The roots of numbers
that you are asked to find in our section were rational, but most have
irrational groups. In particular, the square root of any natural number that is
not perfect square is irrational.
Is numbers like
these cannot be written down exactly posted terminating decimals of fractions,
we often lead then just as they are in calculations and in the answer to
calculations.
The advantage of
this approach is that it allows us to work with exact numbers, rather than
approximations. This is a surd is a numerical expression containing one or more
irrational groups of numbers. × are usually omitted, though sometimes it is
necessary to helpful to include them. Also, wary number and roots are
multiplied together, it is conventional to write the number first. It is also
helpful to write surds in the simplest form possible . You can simplify
describing in this way whenever the number under the square root sign had a
factor that is a perfect square greater than 1.
The square root of a
day was simplified by 1st using the fact that the perfect square
ball is the factor of 80. The working can be shortened by instead using the
fact that the larger perfect square. 16 is a factor of 80.
So the most
efficient to begin with the largest growth factor that you can spot, but it
turns out, is that there is a larger one, then you can simplify the route in
stages. Another way in which you can sometimes simplify surds is to simplify
products to or more square roots. Where different square roots are multiplied
together. You can use the rule.
You can not usually
simplify some of the different such as √3 + √5.
To simplify surds
v
simplify roots of integers
with square factors.
v
Simplify products and
quotients of roots
v
add or subtract roots
that are the same.
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