Presentation is loading. Please wait.

Presentation is loading. Please wait.

Square Roots and Simplifying Radicals

Published byAttila Gáspár Modified over 5 years ago

Similar presentations

Presentation on theme: "Square Roots and Simplifying Radicals"— Presentation transcript:

1 Square Roots and Simplifying Radicals

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

3 Prime Numbers … Perfect Numbers 1, 4, 9, 16, 25, 36, 49…

4 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.

5 Square numbers have perfect roots!

6 Find a perfect number that divides the radicand
EX:1 Find a perfect number that divides the radicand 45= 9*5

7 Find a perfect number that divides the radicand
EX:2 Find a perfect number that divides the radicand 98= 49*2

8 Find a perfect number that divides the radicand
EX:3 Find a perfect number that divides the radicand 48= 4*12

9 Find a perfect number that divides the radicand
EX:4 Find a perfect number that divides the radicand 45= 9*5

10 You try!

11 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

12 15/2 = 7 remainder 1, therefore we leave one variable under the radical

13

14

15

16 Multiplying Radicals

17 Multiplying Radicals Multiply numbers outside the radical with other numbers outside the radical. Multiply radicands with other radicands. Simplify, if possible

18 Example 1 Multiply then simplify if possible.

19 Example 2 Distribute then simplify if possible.

20 Your Turn

21 Add and Subtract Radicals
You can only add or subtract radicals that have the EXACT SAME radicand. Then add/subtract ONLY the number OUTSIDE the radical Then, check to see if you can simplify!!

22 Example 1

23 Example 2 Sometimes you have to simplify 1st then see if you can add.

24 Simplify

25 Simplify

26 Simplify

27 Simplify

28 Simplify

29 Simplify

30 Simplify

31 Simplify

32 Simplify

33 Simplify

34 Simplify

35 Simplify

36 Simplify

Download ppt "Square Roots and Simplifying Radicals"

Similar presentations

Warm-up. EOCT Practice C a)2a (a + 3) ( a + 5) b)2a (a – 3) (a + 5) c)2a (a + 3) (a – 5) d)2a ( a – 3) (a – 5) Which expression is equivalent to 2a 3.

Warm-up. EOCT Practice C a)2a (a + 3) ( a + 5) b)2a (a – 3) (a + 5) c)2a (a + 3) (a – 5) d)2a ( a – 3) (a – 5) Which expression is equivalent to 2a 3.
Simplify:.

Simplify:.
Warm up Simplify. 1. 2. 3..

Warm up Simplify
Simplify, Add, Subtract, Multiply and Divide

Simplify, Add, Subtract, Multiply and Divide
Warm UP!. 16 130 is the Radicand Which number is the radicand?

Warm UP! is the Radicand Which number is the radicand?
Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: 60128 300x 4.

Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: x 4.
11.1 Examples for Simplifying (EX: 1 of 4) Look for factors of 50 that are perfect square numbers. Take the square root of 25. Write it outside the radical.

11.1 Examples for Simplifying (EX: 1 of 4) Look for factors of 50 that are perfect square numbers. Take the square root of 25. Write it outside the radical.
5-6 Radical Expressions Objectives Students will be able to: 1)Simplify radical expressions 2)Add, subtract, multiply, and divide radical expressions.

5-6 Radical Expressions Objectives Students will be able to: 1)Simplify radical expressions 2)Add, subtract, multiply, and divide radical expressions.
Properties and Rules for Exponents Properties and Rules for Radicals

Properties and Rules for Exponents Properties and Rules for Radicals
10-1A Simplifying Radicals Algebra 1 Glencoe McGraw-HillLinda Stamper.

10-1A Simplifying Radicals Algebra 1 Glencoe McGraw-HillLinda Stamper.
Unit 4 Operations & Rules

Unit 4 Operations & Rules
5.5 Roots of Real Numbers and Radical Expressions.

5.5 Roots of Real Numbers and Radical Expressions.
3.6 Solving Quadratic Equations

3.6 Solving Quadratic Equations
R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.

R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.
CCGPS Geometry (12-5-13) UNIT QUESTION: In what ways can algebraic methods be used in problems solving? Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1 Today’s.

CCGPS Geometry ( ) UNIT QUESTION: In what ways can algebraic methods be used in problems solving? Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1 Today’s.
Simplify = 2 = 4 = 5 = 10 = 12.

Simplify = 2 = 4 = 5 = 10 = 12.
Introduction to Irrational Numbers We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational.

Introduction to Irrational Numbers We write “irrational numbers” using a “radical symbol,” often just referred to as a “radical.” √ 3 is an irrational.
Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.

Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.
Simplifying Radicals. Radical Flashback Simplifying Radicals: 1.Find the greatest perfect square that goes into the radicand. 2.Take the square root of.

Simplifying Radicals. Radical Flashback Simplifying Radicals: 1.Find the greatest perfect square that goes into the radicand. 2.Take the square root of.
Multiplying and Simplifying Radicals The Product Rule for Radicals is given by: Note that both of the radicals on the left have the same index. Throughout.

Multiplying and Simplifying Radicals The Product Rule for Radicals is given by: Note that both of the radicals on the left have the same index. Throughout.

Similar presentations

Ads by Google