4.5 SOLVE BY FINDING

SQUARE ROOTSSimplifying Radicals

The Algebra of Solving Equations

SIMPLIFYING RADICALS Test the radicand (number inside the

radical) for divisibility by numbers that are perfect squares.

Rewrite the radicand as a product of a perfect square and another number.

Take the square root of the perfect square and write the result in front of the radical.

FOR EXAMPLE

20

22 423 924 1625 2526 36

4 5

2 5

FOR EXAMPLE

48

22 423 924 1625 2526 36

16 3

4 3

FRACTIONS?

27

49

22 423 924 1625 2526 36

9 3

49

3 3

7

27

49

27 49

OPERATIONS

5 2 3 7

5 3 2 7

15 2 7

15 14

OPERATIONS3 12 2 15

3 4 3 2 15

3 2 3 2 15

6 3 2 15

12 45

12 9 5

36 5

RATIONALIZE THE DENOMINATOR

13

213

2

13

2

2

2

26

4

26

2

RATIONALIZE THE DENOMINATOR

21

621

6

21

6

6

6

126

36

126

6

9 14

6

3 14

6

14

2

SOLVE EQUATIONS (BY FACTORING)

2 81x

2 81 0x

9 9 0x x

9, 9x

SOLVE EQUATIONS (BY SQUARE ROOTS)

2 81x

9, 9x

2 81x

9x

SOLVE EQUATIONS (BY SQUARE ROOTS)

2 40x

2 10, 2 10x

2 40x

2 10x

SOLVE EQUATIONS (BY SQUARE ROOTS)

2 7 43x

5 2, 5 2x

2 50x

5 2x

2 50x

SOLVE EQUATIONS (BY SQUARE ROOTS)

24 11 59x

2 3, 2 3x

2 12x

2 3x

24 48x 2 12x

SOLVE EQUATIONS (BY SQUARE ROOTS)

27 60x

7 2 15, 7 2 15x

27 60x

7 2 15x

7 2 15x

ASSIGNMENTp. 269

# 3 - 10, 22 - 33, 39, 40, 42