Bentuk sederhana dari \(\sqrt[3]{x^2\: \sqrt[4] {\dfrac{1}{x} \sqrt[5] {x^{10}}}}\) adalah …
Jawaban: E
\(\sqrt[3]{x^2\: \sqrt[4] {x^{-1}\cdot x^{\frac{10}{5}}}}\)
\(\sqrt[3]{x^2\: \sqrt[4] {x^{-1}\cdot x^2}}\)
\(\sqrt[3]{x^2\: \sqrt[4] {x^{-1 + 2}}}\)
\(\sqrt[3]{x^2\: {x^{\frac{1}{4}}}}\)
\(\sqrt[3]{x^{2 + \frac{1}{4}}}\)
\(\sqrt[3]{x^{\frac{9}{4}}}\)
\(x^{\frac{9}{12}} = x^{\frac{3}{4}} = \sqrt[4]{x^3}\)
Jawaban: D
\((89 + 2\sqrt{1960})^{\frac{1}{4}}\)
\(\sqrt{\sqrt{(89 + 2\sqrt{1960})}}\)
\(\sqrt{\sqrt{[(49 + 40)+ 2\sqrt{49\times 40}]}}\)
\(\sqrt{\sqrt{49} + \sqrt{40}}\)
\(\sqrt{7 + 2\sqrt{10}}\)
\(\sqrt{(5 + 2) + 2\sqrt{5 \times 2}}\)
\(\sqrt{5} + \sqrt{2}\)
Bentuk sederhana dari \(\dfrac{\sqrt{19 + \sqrt{360}}}{\sqrt{10}\:-\: 3}\) adalah
Jawaban: D
\(\dfrac{\sqrt{19 + 2\sqrt{90}}}{\sqrt{10}\:-\: 3}\)
\(\dfrac{\sqrt{(10 + 9) + 2\sqrt{10 \times 9}}}{\sqrt{10}\:-\: 3}\)
\(\dfrac{\sqrt{10} + \sqrt{9}}{\sqrt{10}\:-\: 3}\)
\(\dfrac{\sqrt{10} + 3}{\sqrt{10}\:-\: 3} \times \color{red} \dfrac{\sqrt{10}+ 3}{\sqrt{10}+ 3}\)
\(\dfrac{(\sqrt{10} + 3)^2}{(\sqrt{10})^2\: – \:3^2}\)
\(\dfrac{10 + 6\sqrt{10} + 9}{10\:-\:9}\)
\(19 + 6\sqrt{10}\)
Nilai \(x\) yang memenuhi persamaan \(\sqrt{x+\sqrt{5x\:-\:9}} + \sqrt{x\:-\:\sqrt{5x\:-\:9}} = 4\) adalah …
Jawaban: E
Kuadratkan kedua ruas,
\(\left(\sqrt{x+\sqrt{5x\:-\:9}} + \sqrt{x\:-\:\sqrt{5x\:-\:9}}\right)\color{red}^2\color{black} = 4\color{red} ^2\)
\(x + \cancel{\sqrt{5x\:-\:9}} + 2\sqrt{(x + \sqrt{5x\:-\:9})(x\:-\:\sqrt{5x\:-\:9})} + \cancel{x\:-\:\sqrt{5x\:-\:9}} = 16\)
\(2x + 2\sqrt{x^2 – (\sqrt{5x\:-\:9})^2} = 16\)
\(2\sqrt{x^2\: – \: 5x + 9} = 16\:-\:2x\:\:\:\:\:\color{blue}\text{bagi kedua ruas dengan 2}\)
\(\sqrt{x^2\: -\: 5x + 9} = 8\:-\:x\)
Kuadratkan kedua ruas lagi,
\(\left(\sqrt{x^2\: -\: 5x + 9}\right)\color{red}^2\color{black} = (8\:-\:x)\color{red}^2\)
\(x^2\: – \: 5x + 9 = 64\: – \:16x + x^2\)
\(\cancel{x^2}\: – \: 5x + 9 = 64\: – \:16x + \cancel{x^2}\)
\(16x\: – \: 5x = 64\: – \:9\)
\(11x = 55\)
\(x = \dfrac{55}{11} = 5\)
