A property of mathematics says that square roots can be distributed over multiplication. That means...
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![Page 1: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/1.jpg)
126
3155
![Page 2: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/2.jpg)
A property of mathematics says that square roots can be
distributed over multiplication.
That means a radical such as
135
can be written as
135
![Page 3: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/3.jpg)
Or a radical expression such as
36can be written as
218
which simplifies to
6
![Page 4: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/4.jpg)
Try these:
100520
1682
10
4
![Page 5: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/5.jpg)
The property is often written:
abbaor
ab ba
![Page 6: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/6.jpg)
A related property says that square roots are also
distributive over division:
ba
ba
![Page 7: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/7.jpg)
ba
ba
or
![Page 8: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/8.jpg)
2
502
50
Simplify:
25 5
3
273
27 9 3
![Page 9: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/9.jpg)
Try one more:
75155 ?
![Page 10: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/10.jpg)
Because 75 is not a perfect square . . .
75155
What makes this one different?
?
. . . we don’t know what its square root is.
We need to do something else to simplify it.
![Page 11: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/11.jpg)
75
One possibility is to get an approximation
from a calculator
66.8
![Page 12: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/12.jpg)
75
But another way to simplify it is to use what we just learned
about multiplying square roots.
325 325
35
![Page 13: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/13.jpg)
75
What just happened?What allowed us to change
to
35 ?
![Page 14: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/14.jpg)
One of our numbers
25was the square root of
a perfect square.
![Page 15: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/15.jpg)
Since we know the square root of perfect squares,
325
we can write
as35
![Page 16: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/16.jpg)
A radical term with all perfect square factors extracted from
the radical is said to be inSimplest Radical Form.
![Page 17: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/17.jpg)
Look at this example:
Is it in simplest radical form?Have all perfect square factors been removed?
96 244 242
![Page 18: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/18.jpg)
No—what is a perfect square factor of 24?
96 244 242
![Page 19: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/19.jpg)
Did you say 4?We need to remove a factor of 4, so we will have:
96 242
You’re right!
642642 622 64
![Page 20: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/20.jpg)
Just like when we simplify fractions,
when we simplify radicals, we are not through until all possible factors
have been removed.
![Page 21: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/21.jpg)
And just like when we simplify fractions,
it saves a step or two if we remove the greatest possible
factor first.
![Page 22: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/22.jpg)
Try this one:
31648 316
34
![Page 23: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/23.jpg)
Try this one:
295185
295253 103
235
![Page 24: A property of mathematics says that square roots can be distributed over multiplication. That means a radical such as can be written as.](https://reader030.fdocuments.us/reader030/viewer/2022032805/56649efa5503460f94c0c863/html5/thumbnails/24.jpg)
Try this one:
3
150 3
150 50
225 25