rasionalkan penyebut pecahan-pecahan berikut a. 3/√5b. 15/√7c.2√2/6√6d. 16√100/1+√32e. 10/5-√2f. 2√5/√3+√5g. 15/√11-√8h. 2√5+2√3/2√5-2-√3
Matematika
laesi
Pertanyaan
rasionalkan penyebut pecahan-pecahan berikut a. 3/√5b. 15/√7c.2√2/6√6d. 16√100/1+√32e. 10/5-√2f. 2√5/√3+√5g. 15/√11-√8h. 2√5+2√3/2√5-2-√3
1 Jawaban
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1. Jawaban ketchup
a. 3/√5 * √5/√5 = 3√5 / 5
b. 15/√7 * √7/√7 = 15√7 / 7
c. 2√2/6√6 * 6√6/6√6
= 12√12 / 216
= √12 / 18
= √4√3 / 18
= 2√3 / 18
d. 16√100/1+√32 = 16*10/1+√32 = 160/1+√32
= 160/1+√32 * 1-√32/1-√32
= (160-160√32) / (1-32)
= (160-(160*√16√2) / (-31)
= (160-(160*4√2) / (-31)
= 160(1-4√2) / (-31)
= 160(4√2-1)/31
e. 10/5-√2 * 5+√2/5+√2
= (50+10√2) / (25-2)
= (50+10√2) / 23
f. 2√5/√3+√5 * √3-√5/√3-√5
= (2√15-2√25) / (3-5)
= (2√15-2*5) / (-2)
= (2√15-10) / (-2)
= -√15+5
g. 15/√11-√8 * √11+√8/√11+√8
= (15(√11+√8)) / 11-8
= (15(√11+√8)) / 3
= 5(√11+√8)
= 5√11+5√8
= 5√11+5√4√2
= 5√11+5*2√2
= 5√11+10√2
h. 2√5+2√3/2√5-2-√3 * 2√5+2+√3/2√5+2+√3
= (20+4√5+2√15+4√15+4√3+6) / (20+4√5+2√15-4√5-4-2√3-2√15-2√3-3)
= (26+4√5+6√15+4√3) / (13-4√3)