Soalan 1:
Hitung nilai bagi setiap yang berikut.
Penyelesaian:
(a)
$$ \begin{aligned} & \sqrt{49}+3^2 \\ & =7+9 \\ & =16 \end{aligned} $$
(b)
$$ \begin{aligned} & \sqrt[3]{27}-1.5^2 \\ & =\sqrt[3]{3 \times 3 \times 3}-(1.5)(1.5) \\ & =3-2.25 \\ & =0.75 \end{aligned} $$
(c)
$$ \begin{aligned} & \sqrt[3]{-64} \times 0.2^3 \\ & =\sqrt[3]{-4 \times-4 \times-4} \times(0.2)(0.2)(0.2) \\ & =-4 \times 0.008 \\ & =-0.032 \end{aligned} $$
(d)
$$ \begin{aligned} & (-2)^2 \div \sqrt{100} \\ & =(-2)(-2) \div \sqrt{10 \times 10} \\ & =4 \div 10 \\ & =0.4 \end{aligned} $$
(e)
$$ \begin{aligned} & \sqrt{2 \frac{1}{4}}-\sqrt[3]{15 \frac{5}{8}} \\ & =\sqrt{\frac{9}{4}}-\sqrt[3]{\frac{125}{8}} \\ & =\frac{3}{2}-\frac{5}{2} \\ & =\frac{-2}{2} \\ & =-1 \end{aligned} $$
(f)
$$ \begin{aligned} \sqrt[3]{\frac{1}{125}} \times 0.3^2 & =\frac{1}{5} \times 0.09 \\ & =0.018 \end{aligned} $$
(g)
$$ \begin{aligned} \sqrt{\frac{12}{27}} \div\left(-\frac{2}{3}\right)^3 & =\sqrt{\frac{4}{9}} \div\left(-\frac{8}{27}\right) \\ & =\frac{2}{3} \times\left(-\frac{27}{8}\right) \\ & =-\frac{9}{4} \end{aligned} $$
(h)
$$ \begin{aligned} & (-5)^2+\sqrt{2 \frac{7}{9}}-2^3 \\ & =25+\sqrt{\frac{25}{9}}-8 \\ & =25+\frac{5}{3}-8 \\ & =17+\frac{5}{3} \\ & =\frac{51}{3}+\frac{5}{3} \\ & =\frac{56}{3} \end{aligned} $$
(i)
$$ \begin{aligned} & (\sqrt{16}-6)^2 \times \sqrt[3]{-\frac{54}{128}} \\ & =(4-6)^2 \times \sqrt[3]{-\frac{27}{64}} \\ & =(-2)^2 \times\left(-\frac{3}{4}\right) \\ & =4 \times\left(-\frac{3}{4}\right) \\ & =-3 \end{aligned} $$
Hitung nilai bagi setiap yang berikut.
Penyelesaian:
(a)
$$ \begin{aligned} & \sqrt{49}+3^2 \\ & =7+9 \\ & =16 \end{aligned} $$
(b)
$$ \begin{aligned} & \sqrt[3]{27}-1.5^2 \\ & =\sqrt[3]{3 \times 3 \times 3}-(1.5)(1.5) \\ & =3-2.25 \\ & =0.75 \end{aligned} $$
(c)
$$ \begin{aligned} & \sqrt[3]{-64} \times 0.2^3 \\ & =\sqrt[3]{-4 \times-4 \times-4} \times(0.2)(0.2)(0.2) \\ & =-4 \times 0.008 \\ & =-0.032 \end{aligned} $$
(d)
$$ \begin{aligned} & (-2)^2 \div \sqrt{100} \\ & =(-2)(-2) \div \sqrt{10 \times 10} \\ & =4 \div 10 \\ & =0.4 \end{aligned} $$
(e)
$$ \begin{aligned} & \sqrt{2 \frac{1}{4}}-\sqrt[3]{15 \frac{5}{8}} \\ & =\sqrt{\frac{9}{4}}-\sqrt[3]{\frac{125}{8}} \\ & =\frac{3}{2}-\frac{5}{2} \\ & =\frac{-2}{2} \\ & =-1 \end{aligned} $$
(f)
$$ \begin{aligned} \sqrt[3]{\frac{1}{125}} \times 0.3^2 & =\frac{1}{5} \times 0.09 \\ & =0.018 \end{aligned} $$
(g)
$$ \begin{aligned} \sqrt{\frac{12}{27}} \div\left(-\frac{2}{3}\right)^3 & =\sqrt{\frac{4}{9}} \div\left(-\frac{8}{27}\right) \\ & =\frac{2}{3} \times\left(-\frac{27}{8}\right) \\ & =-\frac{9}{4} \end{aligned} $$
(h)
$$ \begin{aligned} & (-5)^2+\sqrt{2 \frac{7}{9}}-2^3 \\ & =25+\sqrt{\frac{25}{9}}-8 \\ & =25+\frac{5}{3}-8 \\ & =17+\frac{5}{3} \\ & =\frac{51}{3}+\frac{5}{3} \\ & =\frac{56}{3} \end{aligned} $$
(i)
$$ \begin{aligned} & (\sqrt{16}-6)^2 \times \sqrt[3]{-\frac{54}{128}} \\ & =(4-6)^2 \times \sqrt[3]{-\frac{27}{64}} \\ & =(-2)^2 \times\left(-\frac{3}{4}\right) \\ & =4 \times\left(-\frac{3}{4}\right) \\ & =-3 \end{aligned} $$