Transcript 12.1 Radical Algebraic Expressions 12.2

Sums, Differences, and Products
of Radicals
• There is an easy way to multiply two square
roots. For instance:
• But
9
4 3 26
9  4  36, and 36 is also equal to 6.
Thus, 9
4 94
• Square Root of a Product
– The square root of a product of two
nonnegative numbers equals the product of the
square roots of the two numbers. That is, for
non-negative numbers x and y,
xy  x y
– In other words, square root distributes over
multiplication
This property is useful in
simplifying radicals:
75  25 3
 25
5 3
3
There is NO similar property for
the square root of a sum...
9  16  25
5
Not equal!
9  16  3  4
7
• The only way for two square roots to be
combined by addition or subtraction is for
the radicands to be equal. Thus:
5 3  7 3  12 3
• The process is the same as adding like
terms: 5x + 7x = 12x.
Simplify:
72
72  36 2
6 2
Multiply: 15
7 20
15 7 20  7 300
 7 25  4  3
 7 5 2 3
 70 3
Simplify: 4 6  7 6  6
4 6  7 6  6  2 6
Simplify:
75  48
75  48  25  3  16  3
5 34 3
9 3