Soalan 1:
$$ \text { Diberi } 9261=3^3 \times 7^3 \text {, cari } \sqrt[3]{9261} \text { tanpa menggunakan kalkulator. } $$
Penyelesaian:
$$ \begin{aligned} &\text { Diberi } 9261=3^3 \times 7^3\\ &\begin{aligned} \sqrt[3]{9261} & =\sqrt[3]{3^3 \times 7^3} \\ & =\sqrt[3]{3^3} \times \sqrt[3]{7^3} \\ & =3 \times 7 \\ & =21 \end{aligned} \end{aligned} $$
$$ \text { Diberi } 9261=3^3 \times 7^3 \text {, cari } \sqrt[3]{9261} \text { tanpa menggunakan kalkulator. } $$
Penyelesaian:
$$ \begin{aligned} &\text { Diberi } 9261=3^3 \times 7^3\\ &\begin{aligned} \sqrt[3]{9261} & =\sqrt[3]{3^3 \times 7^3} \\ & =\sqrt[3]{3^3} \times \sqrt[3]{7^3} \\ & =3 \times 7 \\ & =21 \end{aligned} \end{aligned} $$
Soalan 2:
$$ \text { Cari } \sqrt[3]{2744} \text { dengan menggunakan kaedah pemfaktoran perdana. } $$
Penyelesaian:
$$ \begin{aligned} 215 & =2 \times 2 \times 2 \times 7 \times 7 \times 7 \\ & =2 \times 7 \times 2 \times 7 \times 2 \times 7 \\ & =14 \times 14 \times 14 \end{aligned} $$
$$ \begin{aligned} \sqrt[3]{2744} & =\sqrt[3]{14 \times 14 \times 14} \\ & =14 \end{aligned} $$
$$ \text { Cari } \sqrt[3]{2744} \text { dengan menggunakan kaedah pemfaktoran perdana. } $$
Penyelesaian:
$$ \begin{aligned} 215 & =2 \times 2 \times 2 \times 7 \times 7 \times 7 \\ & =2 \times 7 \times 2 \times 7 \times 2 \times 7 \\ & =14 \times 14 \times 14 \end{aligned} $$
$$ \begin{aligned} \sqrt[3]{2744} & =\sqrt[3]{14 \times 14 \times 14} \\ & =14 \end{aligned} $$
Soalan 3:
Cari nilai bagi setiap yang berikut tanpa menggunakan kalkulator.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{27} & =\sqrt[3]{3 \times 3 \times 3} \\ & =3 \end{aligned} $$
(b)
$$ \begin{aligned} \sqrt[3]{-125} & =\sqrt[3]{(-5)(-5)(-5)} \\ & =-5 \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt[3]{343} & =\sqrt[3]{7 \times 7 \times 7} \\ & =7 \end{aligned} $$
(d)
$$ \begin{aligned} \sqrt[3]{-1000} & =\sqrt[3]{(-10)(-10)(-10)} \\ & =-10 \end{aligned} $$
Cari nilai bagi setiap yang berikut tanpa menggunakan kalkulator.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{27} & =\sqrt[3]{3 \times 3 \times 3} \\ & =3 \end{aligned} $$
(b)
$$ \begin{aligned} \sqrt[3]{-125} & =\sqrt[3]{(-5)(-5)(-5)} \\ & =-5 \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt[3]{343} & =\sqrt[3]{7 \times 7 \times 7} \\ & =7 \end{aligned} $$
(d)
$$ \begin{aligned} \sqrt[3]{-1000} & =\sqrt[3]{(-10)(-10)(-10)} \\ & =-10 \end{aligned} $$
Soalan 4:
Cari nilai bagi setiap yang berikut tanpa menggunakan kalkulator.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{\frac{8}{125}} & =\sqrt[3]{\frac{2 \times 2 \times 2}{5 \times 5 \times 5}} \\ & =\sqrt[3]{\left(\frac{2}{5}\right)^3} \\ & =\frac{2}{5} \end{aligned} $$
(b)
$$ \begin{aligned} \sqrt[3]{-\frac{1}{27}} & =\sqrt[3]{\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)} \\ & =\sqrt[3]{\left(-\frac{1}{3}\right)^3} \\ & =-\frac{1}{3} \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt[3]{\frac{24}{81}} & =\sqrt[3]{\frac{8}{27}} \\ & =\sqrt[3]{\left(\frac{2}{3}\right)^3} \\ & =\frac{2}{3} \end{aligned} $$
(d)
$$ \begin{aligned} \sqrt[3]{1 \frac{61}{64}} & =\sqrt[3]{\frac{125}{64}} \\ & =\sqrt[3]{\left(\frac{5}{4}\right)^3} \\ & =\frac{5}{4}=1 \frac{1}{4} \end{aligned} $$
(e)
$$ \begin{aligned} &\begin{aligned} \sqrt[3]{0.001} & =\sqrt[3]{0.1 \times 0.1 \times 0.1} \\ & =0.1 \end{aligned}\\ &\text { AT AU }\\ &\begin{aligned} \sqrt[3]{0.001} & =\sqrt[3]{\frac{1}{1000}} \\ & =\sqrt[3]{\left(\frac{1}{10}\right)^3} \\ & =\frac{1}{10} \\ & =0.1 \end{aligned} \end{aligned} $$
(f)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{-0.064} \\ & =\sqrt[3]{-0.4 \times-0.4 \times-0.4} \\ & =-0.4 \end{aligned}\\ &\text { ATAU }\\ &\begin{aligned} \sqrt[3]{-0.064} & =\sqrt[3]{-\frac{64}{1000}} \\ & =\sqrt[3]{\left(-\frac{4}{10}\right)^3} \\ & =-\frac{4}{10} \\ & =-0.4 \end{aligned} \end{aligned} $$
(g)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{-0.216} \\ & =\sqrt[3]{-0.6 \times-0.6 \times-0.6} \\ & =-0.6 \end{aligned}\\ &A T A U\\ &\begin{aligned} \sqrt[3]{-0.216} & =\sqrt[3]{-\frac{216}{1000}} \\ & =\sqrt[3]{\left(-\frac{6}{10}\right)^3} \\ & =-\frac{6}{10} \\ & =-0.6 \end{aligned} \end{aligned} $$
(h)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{0.000343} \\ & =\sqrt[3]{0.07 \times 0.07 \times 0.07} \\ & =0.07 \end{aligned}\\ &\text { ATAU }\\ &\begin{aligned} \sqrt[3]{0.000343} & =\sqrt[3]{\frac{343}{1000000}} \\ & =\sqrt[3]{\left(\frac{7}{100}\right)^3} \\ & =\frac{7}{100} \\ & =0.07 \end{aligned} \end{aligned} $$
Cari nilai bagi setiap yang berikut tanpa menggunakan kalkulator.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{\frac{8}{125}} & =\sqrt[3]{\frac{2 \times 2 \times 2}{5 \times 5 \times 5}} \\ & =\sqrt[3]{\left(\frac{2}{5}\right)^3} \\ & =\frac{2}{5} \end{aligned} $$
(b)
$$ \begin{aligned} \sqrt[3]{-\frac{1}{27}} & =\sqrt[3]{\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)\left(-\frac{1}{3}\right)} \\ & =\sqrt[3]{\left(-\frac{1}{3}\right)^3} \\ & =-\frac{1}{3} \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt[3]{\frac{24}{81}} & =\sqrt[3]{\frac{8}{27}} \\ & =\sqrt[3]{\left(\frac{2}{3}\right)^3} \\ & =\frac{2}{3} \end{aligned} $$
(d)
$$ \begin{aligned} \sqrt[3]{1 \frac{61}{64}} & =\sqrt[3]{\frac{125}{64}} \\ & =\sqrt[3]{\left(\frac{5}{4}\right)^3} \\ & =\frac{5}{4}=1 \frac{1}{4} \end{aligned} $$
(e)
$$ \begin{aligned} &\begin{aligned} \sqrt[3]{0.001} & =\sqrt[3]{0.1 \times 0.1 \times 0.1} \\ & =0.1 \end{aligned}\\ &\text { AT AU }\\ &\begin{aligned} \sqrt[3]{0.001} & =\sqrt[3]{\frac{1}{1000}} \\ & =\sqrt[3]{\left(\frac{1}{10}\right)^3} \\ & =\frac{1}{10} \\ & =0.1 \end{aligned} \end{aligned} $$
(f)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{-0.064} \\ & =\sqrt[3]{-0.4 \times-0.4 \times-0.4} \\ & =-0.4 \end{aligned}\\ &\text { ATAU }\\ &\begin{aligned} \sqrt[3]{-0.064} & =\sqrt[3]{-\frac{64}{1000}} \\ & =\sqrt[3]{\left(-\frac{4}{10}\right)^3} \\ & =-\frac{4}{10} \\ & =-0.4 \end{aligned} \end{aligned} $$
(g)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{-0.216} \\ & =\sqrt[3]{-0.6 \times-0.6 \times-0.6} \\ & =-0.6 \end{aligned}\\ &A T A U\\ &\begin{aligned} \sqrt[3]{-0.216} & =\sqrt[3]{-\frac{216}{1000}} \\ & =\sqrt[3]{\left(-\frac{6}{10}\right)^3} \\ & =-\frac{6}{10} \\ & =-0.6 \end{aligned} \end{aligned} $$
(h)
$$ \begin{aligned} &\begin{aligned} & \sqrt[3]{0.000343} \\ & =\sqrt[3]{0.07 \times 0.07 \times 0.07} \\ & =0.07 \end{aligned}\\ &\text { ATAU }\\ &\begin{aligned} \sqrt[3]{0.000343} & =\sqrt[3]{\frac{343}{1000000}} \\ & =\sqrt[3]{\left(\frac{7}{100}\right)^3} \\ & =\frac{7}{100} \\ & =0.07 \end{aligned} \end{aligned} $$