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LESSON 1: REAL NUMBERS  RADICALS
Examples Of Radicals:
NOTE: Each of these examples is an irrational
real number.
Properties of Radicals:
Example 1:
Mixed
and Entire Radicals:
Example 2:
Write as mixed radicals.
Solutions:
Example 3:
Write as entire radicals.
Solutions:
Multiplying
Radicals:
Example 4:
Simplify
Solutions:
Addition
and Subtraction of Radicals:
Radicals are added/subtracted just as in ordinary algebra
using LIKE TERMS.
Examples:
2x – 3y + 5x –
6y = 2x + 5x – 3y – 6y = 7x – 9y
Similarly
Example 5:
Simplify
Solutions:
Example 6:
Simplify
Solutions:
Again we
follow the rules of ordinary algebra for expanding
Recall
from ordinary algebra the product of two binomials:
(x + 3)(x + 5) = x(x + 5) + 3(x + 5)
= x^{2} + 5x + 3x + 15
= x^{2}
+ 8x + 15
Division
of Radicals:
Recall
all of the properties of radicals mentioned above:
Example 7:
Simplify
Division
of Radicals with Irrational denominators: Examples:
These are simplified by a
process called rationalizing the denominator.
Example 8:
Simplify by rationalizing the
denominator.
Example 9:
Simplify
Example 10: Simplify
Example 11: Simplify