Question

Bagaimana cara menghitung bentuk akar ini dan berapa hasilnya?
[tex]\displaystyle \frac{\sqrt[3]{2+\sqrt{5}}}{1+\sqrt{5}}[/tex]

Answer 1

Verified answer

Jawab:
[tex]\displaystyle=\bf\frac{1}{2}[/tex]

Penjelasan dgn langkah-langkah:
[tex]\displaystyle\frac{\sqrt[3]{2+\sqrt{5}} }{1+\sqrt{5}}\\\\=\frac{\sqrt[3]{2+\sqrt{5}} }{\sqrt[3]{(1+\sqrt{5})^3}}\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{(1+\sqrt{5})^3}}\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{(1+\sqrt{5})^3}}\\\\\because(p+q)^3=p^3+3p^2q+3pq^2+q^3\therefore\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{1+3\sqrt{5}+3(\sqrt{5})^2+(\sqrt{5})^3}}[/tex]
Selesaikan
[tex]\displaystyle=\sqrt[3]{\frac{2+\sqrt{5}}{1+3\sqrt{5}+3(5)+(\sqrt{5})^2(\sqrt{5})}}\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{1+3\sqrt{5}+15+5\sqrt{5}}}\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{16+8\sqrt{5}}}\\\\=\sqrt[3]{\frac{2+\sqrt{5}}{8(2)+8\sqrt{5}}}\\\\=\sqrt[3]{\frac{\not2+\not\sqrt{5}}{8(\not2+\not\sqrt{5})}}\\\\=\sqrt[3]{\frac{1}{8}}=\frac{\sqrt[3]{1} }{\sqrt[3]{8} }[/tex]
[tex]\displaystyle=\bf\frac{1}{2}[/tex]

(xcvi)