Name: ____________________ Pre- Calc. 10/11 H. Period: _____________

Functions and Equations Chapter 5 – Radical Expressions and Equations

5.1 Working with Radicals

o Convert between mixed radicals and entire radicals. o Compare and order radical expressions. o Identify restrictions on the values for a variable in a radical expression.

5.2 Multiplying and Dividing Radical Expressions

o Perform multiple operations on radical expressions. o Rationalize the denominator. o Solve problems that involve radical expressions.

5.3 Radical Equations

o Solve equations involving square roots. o Determine the roots of a radical equation algebraically. o Identify restrictions on the values for the variable in a radical equation. o Model and solve problems with radical equations.

Name: ____________________ Pre- Calc. 10/11 H. Date: _____________

Chapter 5 – Radical Expressions and Equations Section 5.1 – Working with radicals

Radical review: Identify and define all parts of the radical, then simplify:

35 8

Warm-up 1 - Change to a mixed radical

a) 52 b) 74 m c)

7 463n p d) 8 1132x y e)

3 5 1054a b

Warm-up 2 - Change to an entire radical

a) 4 3 b) 3x x c)

2 32 ( 4 )k k

Warm-up 3- Write another way, then evaluate

a)

1

216 b)

1

516 c)

2

38

SIMPLIFYING RADICAL EXPRESSIONS

A radical expression is simplified when there are no perfect square factors inside the radical;

i.e., when you take as much as you can out of the radical.

Like radicals: ‘Like Radicals’ are radicals with…________________________________________

Example 1: Simplify 3 2 2 2

Verify that the two expressions above are equal: Check with your calculator

Example 2: Simplify

a) 7 3 2 3 b) 3 35 10 6 10 c) 34 2 5 2

Example 3: Simplify

a) 2 75 3 3 b) 27 3 5 80 2 12

c) 9 3 16 ,b b b ≥ 0 d) 3 43 72 100025278324 wwpwp

Restrictions: If the index is even, the radicand must be non-negative, or the radical is undefined.

To find a restriction, set the radicand greater than or equal to zero, then solve.

Example 4: Find the restriction

a) 3 x b) 2 5x c) 3 2x

C

Example 5: What is the exact length of AB?

A B

Example 6: A square is inscribed in a semi-circle. The area of the semi-circle is 150 cm2.

What is the exact perimeter of the square?

0

Assignment: Pg. 278-281 Q# 1-10, 12-17, 19, 22, 25

45° 30°