A surd is a
that is not evaluated, or cannot be precisely evaluated. The
is often a constant, such as the square root of two:
We know that the square root of 2 is 1.4142.. But why do we leave it as a radical and not convert it to the number?
There are a couple of reasons:
It may cancel later
As you are working through a problem, you may get something like:
The surds on the top and bottom cancel leaving
It may get raised to a power later
As you work a problem, you may, for example, end up squaring the surd:
Since root 2 squared is obviously 2, the expression simplifies to
If we had replaced root 2 with 1.414 earlier, we may not notice that squaring it results in exactly 2.
It preserves accuracy
Some radical expressions result in
irrational numbers, with a result that has an infinite number of decimal places.
For example, the square root of 2 is irrational.
No matter how many decimal places you use in the answer, you can always add more and make it more accurate.
We try to leave it as a surd, so so we are not pinning down the accuracy until later when we finally do evaluate it.
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