4- Simplifique os radicais divididos o índice do racional e o...

1. a) √2 + √32 =

1√2 + 4√2 =

(1 + 4)√2 = 5√2.

b) √27 + √3 =

3√3 + 1√3 =

(3 + 1)√3 = 4√3.

c) 3√5 + √20 =

3√5 + 2√5 =

(3 + 2)√5 = 5√3.

d) 2√2 + √8 =

2√2 + 2√2 =

(2 + 2)√2 = 4√2.

2. a) √27 + 5√3 =

3√3 + 5√3 =

(3 + 5)√3 = 8√3.

b) 2√7 + √28 =

2√7 + 2√7 =

(2 + 2)√7 = 4√7.

c) √50 – √98 =

5√2 – 7√2 =

(5 – 7)√2 = – 2√2.

d) √12 – 6√3 =

2√3 – 6√3 =

(2 – 6)√3 = – 4√3.

3. a) √28 – 10√7 =

2√7 – 10√7 =

(2 – 10)√7 = – 8√7.

b) 9√2 + 3√50 =

9√2 + 3 · (5√2) =

9√2 + 15√2 =

(9 + 15)√2 = 24√2.

c) 6√3 + √75 =

6√3 + 5√3 =

(6 + 5)√3 = 11√3.

d) 2√50 + 6√2 =

2 · (5√2) + 6√2 =

10√2 + 6√2 =

(10 + 6)√2 = 16√2.

4. a) √98 + 5√18 =

7√2 + 5 · (3√2) =

7√2 + 15√2 =

(7 + 15)√2 = 22√2.

b) 3√98 – 2√50 =

3 · (7√2) – 2 · (5√2) =

21√2 – 10√2 =

(21 – 10)√2 = 11√2.

c) 3√8 – 7√50 =

3 · (2√2) – 7 · (5√2) =

6√2 – 35√2 =

(6 – 35)√2 = – 29√2.

d) 2√32 – 5√18 =

2 · (4√2) – 5 · (3√2) =

8√2 – 15√2 =

(8 – 15)√2 = – 7√2.

5. a) √75 – 2√12 + √27 =

5√3 – 2 · (2√3) + 3√3 =

5√3 – 4√3 + 3√3 =

(5 – 4 + 3)√3 =

(8 – 4)√3 = 4√3.

b) 2√7 + √28 =

2√7 + 2√7 =

(2 + 2)√7 = 4√7.

c) √50 – √98 =

5√2 – 7√2 =

(5 – 7)√2 = – 2√2.

d) √12 – 6√3 =

2√3 – 6√3

(2 – 6)√3 = – 4√3.