Question

A. keliling sebuah persegi panjang (16 + 8 √2) cm, sedangkan panjangnya (6+√2) cm. lebar persegi panjang tersebut.... cm.

b. if a = √3 + √2 and b = √3 - √2then the result of a² - b² is...

c. sederhanakan oprasi akar berikut.
◎ √20 ( √15 + √40 - √45)
◎ (√6 + √3)²
◎(2√2 + 1)(√2 - 3)

tolong bantu.... besok harus di kumpulkan..
ini sulit tolong bantu aku
juseyo ^_^

Answer 1

A) k = (16 + 8√2)
p = (6 + √2)
k = 2 × (p + l)
(16 + 8√2) = 2 × {(6 + √2)+l}
2(8 + 4√2) = 2×{(6 + √2)+l}
l = (8 + 4√2) - (6 + √2)
l = 8 - 6 + 4√2 - √2
l = (2 + 3√2) cm

b) a² - b² = (a + b)(a - b)
= (√3 + √2)(√3 - √2)
= √9 + √6 - √6 - √4
= 3 - 2
= 1

c) √20(√15 + √40 - √45)
= √300 + √800 - √900
= 10√3 + 20√2 - 30
= 10(√3 + 2√2 - 3)

(√6 + √3)²
= (√6)² + 2.√6.√3 + (√3)²
= 6 + 2√18 + 3
= 9 + 6√2
= 3 (3 + 2√2)

(2√2 + 1)+(√2 - 3)
= (2√2.√2) + (1.√2) - (3.2√2) + (-3.1)
= 2√4 + √2 - 6√2 - 3
= 4 - 3 +√2 - 6√2
= 1 - 5√2

Answer 2

A)
K = 16+8√2
2.(p+l) = 16+8√2
2.(6+√2 + l) = 16+8√2
12+2√2+2l = 16+8√2
2l = 16-12+8√2-2√2
2l = 4+6√2
l = (4+6√2) : 2
l = (2+3√2) cm


b)
a²-b²
= (√3+√2)²-(√3-√2)²
= √9+2.√3.√2+√4-(√9+2.√3.(-√2)+√4)
= 3+2√6+2-(3-2√6+2)
= 3+2+2√6-3+2√6-2
= 3+2-3-2+2√6+2√6
= 4√6


c)
√(4.5) . (√15 + √(4.10) - √(9.5)
= 2√5 . (√15 + 2√10 - 3√5)
= 2√75 + 4√50 - 6√25
= 2√(25.3) + 4√(25.2) - 6.5
= 2.5√3 + 4.5√2 + 30
= 10√3 + 20√2 + 30
= 10.(√3+2√2+3)



(√6+√3)²
= (√6)²+2.√6.√3+(√3)²
= √36+ 2√18+√9
= 6+2√18+3
= 6+3+2√18
= 9+2√(9.2)
= 9+2.3√2
= 9+6√2
= 3.(3+2√2)




(2√2+1).(√2-3)
= 2√2.√2 + 2√2.(-3) + 1.√2 + 1.(-3)
= 2√4 - 6√2 + √2 - 3
= 2.2 - 5√2 - 3
= 4 - 3 - 5√2
= 1 - 5√2