Hasil perhitungan dari: (48^(1/2) - 2 18^(1/2) + 75^(1/2) +

$3\sqrt{3} + 7\sqrt{2}$

Pembahasan

Pertama, kita sederhanakan setiap suku akar kuadrat:
$48^{1/2} = \sqrt{16 \times 3} = 4\sqrt{3}$
$18^{1/2} = \sqrt{9 \times 2} = 3\sqrt{2}$
$75^{1/2} = \sqrt{25 \times 3} = 5\sqrt{3}$
$50^{1/2} = \sqrt{25 \times 2} = 5\sqrt{2}$
$27^{1/2} = \sqrt{9 \times 3} = 3\sqrt{3}$
$125^{1/2} = \sqrt{25 \times 5} = 5\sqrt{5}$
$169^{1/2} = \sqrt{169} = 13$
$45^{1/2} = \sqrt{9 \times 5} = 3\sqrt{5}$
$20^{1/2} = \sqrt{4 \times 5} = 2\sqrt{5}$
$576^{1/2} = \sqrt{576} = 24$

Sekarang, substitusikan kembali ke dalam pecahan:

Pembilang: $4\sqrt{3} - 2(3\sqrt{2}) + 5\sqrt{3} + 4(5\sqrt{2}) - 3\sqrt{3}$
$= 4\sqrt{3} - 6\sqrt{2} + 5\sqrt{3} + 20\sqrt{2} - 3\sqrt{3}$
Kelompokkan suku-suku yang sejenis:
$= (4\sqrt{3} + 5\sqrt{3} - 3\sqrt{3}) + (-6\sqrt{2} + 20\sqrt{2})$
$= (4+5-3)\sqrt{3} + (-6+20)\sqrt{2}$
$= 6\sqrt{3} + 14\sqrt{2}$

Penyebut: $5\sqrt{5} + 2(13) + 3\sqrt{5} - 4(2\sqrt{5}) - 24$
$= 5\sqrt{5} + 26 + 3\sqrt{5} - 8\sqrt{5} - 24$
Kelompokkan suku-suku yang sejenis:
$= (5\sqrt{5} + 3\sqrt{5} - 8\sqrt{5}) + (26 - 24)$
$= (5+3-8)\sqrt{5} + 2$
$= 0\sqrt{5} + 2$
$= 2$

Jadi, hasil perhitungan pecahannya adalah:
$\frac{6\sqrt{3} + 14\sqrt{2}}{2}$
$= \frac{2(3\sqrt{3} + 7\sqrt{2})}{2}$
$= 3\sqrt{3} + 7\sqrt{2}$