Question

Rasionalkan bentuk akar berikut dan ubahlah menjadi bentuk yang paling sederhana


[tex] \frac{4 \sqrt{3} }{2 \sqrt{3} - 3 } [/tex]

Answer 1

Verified answer

Jawab:
[tex]=\bf8+4\sqrt{3}[/tex]

Penjelasan dengan langkah-langkah:
[tex]\displaystyle Rasionalkan\:\:\:\frac{4\sqrt3}{2\sqrt3-3}\\\\\because\frac{a}{b-c}=\frac{a(b+c)}{b^2-c^2}\therefore\\\\\frac{4\sqrt3}{2\sqrt3-3}=\frac{4\sqrt3(2\sqrt3+3)}{(2\sqrt3)^2-3^2}\\\\=\frac{4\sqrt3(2\sqrt3)+4\sqrt3(3)}{2^2(\sqrt3)^2-3^2}\\\\=\frac{4(2)(\sqrt3)^2+4(3)\sqrt3}{4(3)-3(3)}\\\\=\frac{8(3)+4(3)\sqrt3}{3(4-3)}=\frac{3(8+4\sqrt{3})}{3(4-3)}\\\\=\frac{\not3(8+4\sqrt{3})}{\not3(4-3)}=\frac{8+4\sqrt{3}}{1}\\=\bf8+4\sqrt{3}[/tex]

(xcvi)

Answer 2

[tex]\frac{4 \sqrt{3} }{2 \sqrt{3} - 3 } = [/tex]

[tex] \frac{4 \sqrt{3} }{2 \sqrt{3} - 3 }· \frac{2 \sqrt{3} + 3 }{2 \sqrt{3} + 3 } = [/tex]

[tex] \frac{(4 \sqrt{3})(2 \sqrt{3} + 3) }{(2 \sqrt{3} - 3)(2 \sqrt{3} + 3) } = [/tex]

[tex] \frac{4 \sqrt{3} ·2 \sqrt{3} + 4 \sqrt{3}·3 }{2 \sqrt{3} (2 \sqrt{3} + 3) - 3(2 \sqrt{3} + 3)} = [/tex]

[tex] \frac{4·2·3 + 12 \sqrt{3} }{4·3 + 6 \sqrt{3} - 6 \sqrt{3} - 9 } = [/tex]

[tex] \frac{24 + 12 \sqrt{3} }{12 + 6 \sqrt{3} - 6 \sqrt{3} - 9 } = [/tex]

[tex] \frac{24 + 12 \sqrt{3} }{12 - 9} = [/tex]

[tex] \frac{24 + 12 \sqrt{3} }{3} = [/tex]

[tex]8 + 4 \sqrt{3} [/tex]