Question

1.Sederhanakan
a.√8 x √12
b.(5+√5)^2
c.3√175/5
d.4√20/2√5
e.6√48-3√12+5√27
f.(6√3-2√2)(6√3+2√2)
g.(3√5+4√2)^2

2.Rasionalkan
a.3√2 /√5
b.√3 /5+√7
c.1+3√2 / √3-√5
d.√7-√5 / √5-√8
e.3√5-5√3 / 5√3+3√5​

Answer 1

Verified answer

Penjelasan dengan langkah-langkah:

1. a. √8 x √12 = √(4.2) x √(4.3) = 2√2 x 2√3 = 4√6

b. (5+√5)² = 5² + 5.2.√5 + (√5)² = 25 + 10√5 + 5 = 30 + 10√5

c. 3√175 ÷ 5 = 3√(25.7) ÷ 5 = 3.5√7 ÷ 5 = 3√7

d. 4√20 ÷ 2√5 = (4÷2)(√20 ÷ √5) = 2√4 = 2.2 = 4

e. 6√48 - 3√12 + 5√27 = 6√(16.3) - 3√(4.3) + 5√(9.3) = 6.4√3 - 3.2√3 + 5.3√3 = 24√3 - 6√3 +15√3 = 33√3

f. (6√3 - 2√2) (6√3 + 2√2) = (6√3)² _ (2√2)² = 108 - 8 = 100

g. (3√5 + 4√2)² = (3√5)² + 2.3√5.4√2 + (4√2)² = 45 + 24√′10 + 32 = 77 + 24√10

2. a. 3√2 ÷ √5 = 3√2/√5 x √5/√5 = 3√10/5 = (3/5)√10

b. √3 /(5+√7) = √3 /(5+√7) x (5 -√7)/(5-√7) = √3 (5-√7)/(25-7) = √3(5-√7)/18

c. (1 + 3√2) / (√3 -√5) = (1+3√2) / (√3-√5) x (√3+√5)/(√3+√5) = {(1+3√2)(√3+√5)}/(3-5) = (√3+√5+3√6+3√10)/(-2)

d. (√7-√5)/(√5-√8) = (√7-√5)/√5-√8) x (√5+√8)/(√5+√8) = {(√7-√5)(√5+√8)}/(5-8) = {(√7-√5)(√5+√8)}/(-3)

e. (3√5-5√3)/(5√3+3√5) = (3√5-5√3)/(5√3+3√5) x (5√3-3√5)/(5√3-3√5) = {(3√5-5√3)(5√3-3√5)}/(75-45) = 15√15-45-75+15√15)/30 = (30√15-120)/30 = √15 - 4