Worksheet Key 2/23/2019 9:20 PM Simplifying Radicals.

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Presentation transcript:

Worksheet Key 2/23/2019 9:20 PM Simplifying Radicals

Grade Distribution 1st 4th 7th 9th A 9 2 5 B 8 11 4 C 6 D 3 F 7 D 3 F 7 No Show 1 100+ Range 48-105 45-99 52-103 41-95 Avg 79.3 76.1 80.56 72.31

SIMPLIFYING RADICAL EXPRESSIONS 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

Radicals are a way to symbolized a number being rooted Definitions Square Roots are a number that when squared (multiplied by itself) is equal to the given number Radicals are a way to symbolized a number being rooted 2/23/2019 9:20 PM Simplifying Radicals

Root Radical Sign Base Review Identifying radicals Unless noted, we must assume the root is 2 Base

Review Identifying radicals 2/23/2019 9:20 PM Simplifying Radicals

10.3 - Simplifying Radical Expressions STEPS Identify the root and the base Breakdown the base to prime and group them into roots OR perfect roots into radical form Combine all the same radicals (for example if √5 and √5 comes out, drop off the radical and keep the number [5]) Multiply the bases and radicals together 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 1 Simplify Identify the root and base Root Base 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 1 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 2 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 3 Simplify Identify the root and base Root Base 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 3 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 4 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 5 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 6 Simplify Identify the root and base(s) Root Bases 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions EXAMPLE 6 Simplify Combine like terms if necessary and multiply. 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Review Simplify 3x • 4x 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

Steps for Multiplying/Dividing Multiply only with the same indexes Reduce radicals to proper simplified form Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 7 Simplify 3√2 • 2√2 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 8 Simplify 2√3 • 4√12 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

EXAMPLE 9 Simplify 2/23/2019 9:20 PM Radical Operations

10.3 - Simplifying Radical Expressions Example 10 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

EXAMPLE 11 Simplify REMEMBER: No radicals in the denominator; we must multiply by the radical in denominator 2/23/2019 9:20 PM Radical Operations

10.3 - Simplifying Radical Expressions Review Simplify 3x + 4x 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

Add/Subtract Radicals Reduce radicals to proper simplified form Combine like terms Simplify, if needed 2/23/2019 9:20 PM Radical Operations

10.3 - Simplifying Radical Expressions Example 12 Add 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 13 Add 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 14 Subtract 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Subtract 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 15 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Example 16 Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

10.3 - Simplifying Radical Expressions Your Turn Simplify 2/23/2019 9:20 PM 10.3 - Simplifying Radical Expressions

EXAMPLE 17 Simplify 2/23/2019 9:20 PM Radical Operations

EXAMPLE 18 Simplify 2/23/2019 9:20 PM Radical Operations

YOUR TURN Simplify 2/23/2019 9:20 PM Radical Operations

Review Multiply FOIL

Example 19 Multiply What’s another way of re-writing this?

Example 20 Multiply 2/23/2019 9:20 PM Multiplying Radicals

Your Turn Multiply

Example 21 Multiply

Your Turn Multiply