Matematika

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

  • 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)

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