ExerciseExerciseSimplify 5x + 3y – x + 10y. Simplify 5x + 3y – x + 10y.

4x + 13y4x + 13y

Simplify 74 – 5m – 2m – 8.Simplify 74 – 5m – 2m – 8.

– 7m + 66– 7m + 66

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Simplify 14w + 23 – 16n.Simplify 14w + 23 – 16n.

already in simplified formalready in simplified form

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Simplify 17t – 6q + t + 8r. Simplify 17t – 6q + t + 8r.

– 6q + 8r + 18t– 6q + 8r + 18t

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Which property is used to add like terms?Which property is used to add like terms?

Distributive PropertyDistributive Property

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2x + 5x2x + 5x

2 √ 7 + 5 √ 72 √ 7 + 5 √ 7

√ a √ b = √ ab√ a √ b = √ ab

√ a + √ b ≠ √ a + b√ a + √ b ≠ √ a + bbutbut

Simplify 6 √ 7 + 3 √ 2 – 2 √ 7.Simplify 6 √ 7 + 3 √ 2 – 2 √ 7.

6 √ 7 + 3 √ 2 – 2 √ 76 √ 7 + 3 √ 2 – 2 √ 7= 6 √ 7 – 2 √ 7 + 3 √ 2 = 6 √ 7 – 2 √ 7 + 3 √ 2 = (6 – 2) √ 7 + 3 √ 2 = (6 – 2) √ 7 + 3 √ 2 = 4 √ 7 + 3 √ 2 = 4 √ 7 + 3 √ 2

Example 1Example 1

Simplify 4 √ 2 – 3 √ 5 + 2 √ 7.Simplify 4 √ 2 – 3 √ 5 + 2 √ 7.

No simplification is possible. Unlike terms cannot be

simplified further.

No simplification is possible. Unlike terms cannot be

simplified further.

Example 2Example 2

Simplify 3 √ 5 + 2 √ 5.Simplify 3 √ 5 + 2 √ 5.

5 √ 55 √ 5

ExampleExample

Simplify 5 √ 11 + 3 √ 11.Simplify 5 √ 11 + 3 √ 11.

8 √ 118 √ 11

ExampleExample

Simplify 2 √ 3 + 3 √ 2 – 5 √ 2.Simplify 2 √ 3 + 3 √ 2 – 5 √ 2.

2 √ 3 – 2 √ 2 2 √ 3 – 2 √ 2

ExampleExample

Simplify 8√5 + 2√6 – √5 + 3√6.Simplify 8√5 + 2√6 – √5 + 3√6.

7 √ 5 + 5 √ 6 7 √ 5 + 5 √ 6

ExampleExample

Simplify 3 √ 2 + 2 √ 5 – 3 √ 3.Simplify 3 √ 2 + 2 √ 5 – 3 √ 3.

3 √ 2 + 2 √ 5 – 3 √ 33 √ 2 + 2 √ 5 – 3 √ 3

ExampleExample

Simplify 5 √ 12 + 3 √ 12 – √ 12.Simplify 5 √ 12 + 3 √ 12 – √ 12.

14 √ 314 √ 3

ExampleExample

2 √ 12 + 8 √ 32 √ 12 + 8 √ 3

Simplify √ 27 + √ 12.Simplify √ 27 + √ 12.

√ 27 + √ 12√ 27 + √ 12= √ 3 × 3 × 3 + √ 2 × 2 × 3 = √ 3 × 3 × 3 + √ 2 × 2 × 3

= (3 + 2) √ 3 = (3 + 2) √ 3

= 5 √ 3= 5 √ 3

= 3 √ 3 + 2 √ 3 = 3 √ 3 + 2 √ 3

Example 3Example 3

Simplify 3√ 8 – 2 √ 18 – √ 12 + 4 √ 50.Simplify 3√ 8 – 2 √ 18 – √ 12 + 4 √ 50.= 3 √ 2 × 2 × 2 + 2 √ 2 × 3 × 3 –

√ 2 × 2 × 3 + 4 √ 2 × 5 × 5= 3 √ 2 × 2 × 2 + 2 √ 2 × 3 × 3 –

√ 2 × 2 × 3 + 4 √ 2 × 5 × 5= 6 √ 2 – 6 √ 2 – 2 √ 3 + 20 √ 2= 6 √ 2 – 6 √ 2 – 2 √ 3 + 20 √ 2= (6 – 6 + 20) √ 2 – 2 √ 3 = (6 – 6 + 20) √ 2 – 2 √ 3 = 20 √ 2 – 2 √ 3= 20 √ 2 – 2 √ 3

Example 4Example 4

Simplify 3 √ 12 + 2 √ 75.Simplify 3 √ 12 + 2 √ 75.

16 √ 316 √ 3

ExampleExample

Simplify 5 √ 2 + 3 √ 8 – √ 32.Simplify 5 √ 2 + 3 √ 8 – √ 32.

7 √ 27 √ 2

ExampleExample

Simplify 3 √ 2 (√ 18 + √ 50 ).Simplify 3 √ 2 (√ 18 + √ 50 ).

4848

ExampleExample

Simplify .Simplify .5 √ 12 + 3 √ 275 √ 12 + 3 √ 27

√ 3√ 3

1919

ExampleExample

Simplify 3 √ 2 (2 √ 3 + 4 √ 2 ).Simplify 3 √ 2 (2 √ 3 + 4 √ 2 ).

6 √ 6 + 24 6 √ 6 + 24

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Simplify √ 6 (3 √ 7 – 5 √ 3 ).Simplify √ 6 (3 √ 7 – 5 √ 3 ).

3 √ 42 – 15 √ 2 3 √ 42 – 15 √ 2

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Simplify √ 24 ( √ 30 + √ 6 ).Simplify √ 24 ( √ 30 + √ 6 ).

12 √ 5 + 12 12 √ 5 + 12

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Simplify 4√ 12 (3√ 32 + 5√ 18 ).Simplify 4√ 12 (3√ 32 + 5√ 18 ).

216 √ 6216 √ 6

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Simplify .Simplify .7 √ 15 – 2 √ 157 √ 15 – 2 √ 15

√ 15√ 15

55

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Simplify .Simplify .10 √ 26 – 5 √ 3910 √ 26 – 5 √ 39

5 √ 135 √ 13

2 √ 2 – √ 32 √ 2 – √ 3

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