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When you take the
of a whole number, you either get another whole number (e.g.
) or you get an
). Be careful when adding with irrational numbers:
an expression like
can't be simplified. It's already in simplest form. On the other hand, you can use the
to group like radicals:
Irrational numbers can sometimes be simplified by factoring out a
from the radicand (the part under the square root sign.) First, you need to know this important property:
For all real numbers
That is, the square root of the product is the same as the product of the square roots.
There's an analogous quotient property:
For all real numbers
The idea here is to find a perfect square factor of the radicand, write the radicand as a product, and then use the product property to simplify.
9 is a perfect square, which is also a factor of 45.
Use the product property.
When you have variables under the radical sign, see if you can factor out a square.
We can factor the radicand as the product of
and a squared expression.
Use the product property of square roots:
Use absolute value symbols and simplify the given radical form.
Simplify and verify your answer using a calculator.
Find the area of the rectangle with
length = √ 24 and breadth = √ 8.
Compare the given pair of terms using
, or equal.
is power (in watts) and
is resistance (in ohms), then the voltage
necessary to run the circuit is
Find the voltage necessary to run a 40–watt amplifier with a resistance of 150 ohms.
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