Square Roots and Simplifying Radicals

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Presentation transcript:

Square Roots and Simplifying Radicals

Radical Sign (square root sign) Radicand Numbers or variables under the radical sign

Prime Numbers 2 3 5 7 11 13…

Radicals are in SIMPLEST form when: 1. No perfect square factors other than 1 are under the radical. No fractions are under the radical. No radicals are in the denominator.

You’ll need to know how to prime factor to simplify square roots. If a radicand isn’t a perfect square, you’ll prime factor. List some prime factors.

Factor Trees to Prime Factorization 45

Factor Trees to Prime Factorization 54

Factor Trees to Prime Factorization 98

When you have a pair, bring the number out. EX:1 Simplify. When you have a pair, bring the number out.

When you have a pair, bring the number out. EX:2 Simplify When you have a pair, bring the number out.

EX:3

EX:4 Simplify.

You try! 5. 6. 7. 8.

Variables as Radicands Even Exponent – ODD Exponent – Take HALF out (nothing left under the radical) Leave ONE under the radical and take HALF of the rest out

When you have a pair, bring that term out. EX:9 VARIABLES When you have a pair, bring that term out.

When you have a pair, bring that term out. EX:10 VARIABLES When you have a pair, bring that term out.

When you have a pair, bring that term out. Prime Factor EX:11 VARIABLES 2 18 3 9 3 When you have a pair, bring that term out.

Classwork: Finish back of sheet Homework: Stupid Puzzle