Algebra 2: Section 5.3

Solving Quadratic Equations by Finding

Square Roots

Definitions

• Radical sign

• Radicand

– Number under radical sign

• Radical

– Expression itself is the radical

16, 16 is radicand, 16 is radical

Simplifying Radicals

• Find the largest factor of the radicand

that is a perfect square

• Take square root of the perfect square

factor

• Other factor stays under radical

Simplify the Expressions

1. 500

100 5

10 5

What is largest perfect

square that divides

evenly into 500?

First radical: perfect square

Second radical: other factor

Square root of 100 is 10.

Simplify the Expressions

2. 3 12 6

3 4 3 6

3 2 3 6

6 18

6 9 2

6 3 2

18 2

Method 2

3 72

3 36 2

3 6 2

18 2

Rationalizing Denominator

• Cannot have radicals in denominator

• To remove radicals from denominator:

– Simplify all radicals

– Multiply top and bottom by radical in

denominator

Simplify the Expressions

3. 25

3

25

3

5

3

3

3

5 3

9

5 3

3

Simplify the Expressions

4. 2

11

2

11

11

11

22

121

22

11

Solving Quadratics(By Isolating)

• Get the term that is squared by itself

• Take square root of both sides

– Be sure to include positive and negative

answers

• Get x by itself if necessary

Solve5. 3 5x2 9

25 12x

2 12

5x

12

5x

12

5

4 3 2 3

5 5

2 3 5

5 5

2 15

5

Solve26. 3( 2) 7 28x

2( 2) 7x

2 7x

2 7x

23( 2) 21x

Solve

7. 1

5x 4

26

24 30x

4 30x

4 30x

Assignment

• p.267

20-68 evens

(25 problems)

• Math Journal

Wind Pressure and Building Codes

p.269 #74