Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Aim: How can We Add and Subtract Radicals?

Do Now:

Simplify: 7 672a b

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Model Problems

Simplify:4 345a b

3 616x

2 2 29 5( )a b b

23 5a b b

2 33 8 2( )x

2 32 2x

2 2 29 5( )a b b

2 333 38 2 ( )x

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Addition

xy 24 Not like terms - can’t be combined

4

1

8

3

8

5

8

2

8

3

5424 9646

22 35 bb 22 8)35( bb

15153 15415)13(

1115 Not like radicals - can’t be combined

6362

5 6

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Addition

2

1

4

1

Find Common Denominator

4

3

4

2

4

1

2

1

4

1

8020 ?Find Common Radicand

Simplify!

51654 5452

56

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Rules for Addition of Radicals

7527

32539 3533 38

Simplify each to a Common RadicandSimplify each to a Common Radicand

Note: Not all radicals can be simplified to like radicals

2445 6459 6253 This expression cannot be simplified

or combined any further

Add the coefficients and place the sum in front of the Common Radical

Add the coefficients and place the sum in front of the Common Radical

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Rules in General for Adding & Subtracting

•Must have same radicand

•Must have the same index

•Add or subtract coefficients and combine result with the common radical

Combined Result

Coefficient

3533 Common Radical

38

•Unlike radicals must first be simplified to obtain like radicals,

if possible.

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Model Problems

Subtract:

403902 Simplify (find a perfect square factor)

10431092 10431092

10231032 106106

0

Simplify: 753108275 3253336395

3253336395 35336335

31536315 3243)15615(

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Model Problems

Simplify:3 3 364 8 27x x x

3 3 33 3 34 2 3x x x 3 3 33 3 33 3 34 2 3x x x

3 3 34 2 3x x x 35 x

8 5 3 20( ) ( )

8 3 5 20

11 5 4 5

11 5 2 5 11 5

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Model Problem

Find the perimeter of the figure below:

4,0

0,4

-4,0

0,-4

d (x2 x1 )2 ( y2 y1 )2

Shape: ? square

1side (4 0)2 (0 4)2

1side 42 ( 4)2 32

Perimeter = 4 x length of 1 side

4(4 2) 16 2

32 16 2 4 2

Aim: Add & Subtract Radicals Course: Adv. Alg. & Trig.

Model Problem

The ratio of the length towidth of this paintingis approximately equal tothe golden ratio

(1 5) : 2

The width of the painting is 50 inches. Findits length.

length

width

1 5

2

length(l)

50

2l 50 50 5

l 50 50 5

2

l 25 25 5 81 in.