When you take the square root of a whole number, you either get another whole number (e.g.
) or you get an irrational number (e.g.
). 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 distributive law to group like radicals:
Irrational numbers can sometimes be simplified by factoring out a perfect square from the radicand (the part under the square root sign.) First, you need to know this important property:
For all real numbers a and b,
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 a and b, b ≠ 0:
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 a 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.
If P is power (in watts) and R is resistance (in ohms), then the voltage V necessary to run the circuit is
Find the voltage necessary to run a 40–watt amplifier with a resistance of 150 ohms.