Download 11pc sec 2.2 – Working w Radicals

Pre-Calculus 11
Section 2.2: Simplifying Radical Expressions
Date: _____________________
Page 1 of 3
Review from Math 10: Parts of a radical
Recall: Connection between Radical and Fractional exponent
Note: the radical symbol only represents the _____________ square root, so
25  ______  ______
72 and 3 128 are called ______________ radicals (everything underneath the
symbol) whereas
6 2 and 43 2 are called _______________ radicals (a product of a monomial and a radical.
Entire Radical: No coefficient (except negative 1 or 1)
Mixed Radical:
When possible, reduce entire radical to mixed radical with the smallest possible radicand. Also,
rationalize the denominator so that the radicand is not a fraction.
Pre-Calculus 11
Section 2.2: Simplifying Radical Expressions
Date: _____________________
Page 2 of 3
Example 1: Convert entire radicals to mixed radicals… (see if you can do it two ways)
3
54x10
a) 150
b)
Method 1: Prime factorization
Method 1: Prime factorization
Method 2: Greatest-Perfect Square Factor
Method 2: Greatest-Perfect Cube Factor
c)
72a 5b 4 c11 (use whichever method you like)
NOTE: Examples b and c have variables in the
radicand….do we need to be concerned by that?
_______!!!. If a radical represents a real
number and has an ________ index, then the
______________ must be _________________.
Note: A radical is in SIMPLEST form when the radicand does not contain a fraction or any factor
which may be removed.
Example 2: Put the following numbers in order from least to greatest (no calculator use here!)
1
14
511 2
205
10 2
Solution: Write as entire radical.
Pre-Calculus 11
Section 2.2: Simplifying Radical Expressions
Date: _____________________
Page 3 of 3
Example 3: Convert mixed radicals to entire radicals. Now also identify the values of the variable for
which the radical represents a real number for parts c and d!
b) 10 3 2
d)  4a 2 b 3 2ab
a) 5 3
c) x 5 2 x
Home Learning: 2.2 page 100, #3,4,5b,6b,7a,8c,9(choose 1), 10 (choose 1), 11, (choose 1), 16a, do the
study notes. Go over Checkpoint 1 on page 107, Higher Level: 12, 14, 16b