Page 32 - E-MODUL FUNGSI EKSPONENSIAL DAN LOGARITMA X AISYAH AMINI

5. 4√20 − 2√45

6. 4√6(√3 + 5√2)
7. (3√2 + √6)(3√2 − √6)

Penyelesaian:

1. √48 = √16 × 3 = √16 × √3 = 4√3
2. 2√162 = 2√81 × 2 = 2√81 × √2 = 2 × 9 × √2 = 18√2

3. 5√3 + 2√3 = 7√3
4. √108 + √48 = √36 × 3 + √16 × 3 = 6√3 + 4√3 = 10√3

5. 4√20 − 2√45 = 4√4 × 5 − 2√9 × 5 = 4 × 2√5 − 2 × 3√5 = 8√5 −

6√5 = 2√5

6. 4√6(√3 + 5√2) = 4√6 × √3 + 4√6 × 5√2 = 4√9 × 2 + 20√4 × 3 =
4 × 3√2 + 20 × 2√3 = 12√2 + 40√3

2
7. (3√2 + √6)(3√2 − √6) = (3√2) − 3√2 × √6 + 3√2 × √6 −
2
2
2
(√6) = (3√2) − (√6) = 18 − 6 = 12

Sederhanakanlah dan nyatakan dalam bentuk akar

1 2
2
1. ( 3 . 2)
5 2
3
2. ( 4 . 4)

Penyelesaian :

2 1 2 2 1 2 4 3 2 7 2 7
1. ( 3 . 2) = ( 3 2) = ( 6 6) = ( 6) = 3 = √ = . √
+
3
+
3
2
7
3 5 2 3 5
2. ( 4 . 4) = 2 . 2 = √ . = √
2
5
3

12