Soalan 6:
Gambar foto di sebelah menunjukkan sebuah kotak hiasan yang berbentuk kubus. Setiap luas permukaan kotak itu ialah 2 500 mm2.
(a) Cari panjang tepi, dalam mm, kotak hiasan itu.
(b) Tulis isi padu kotak hiasan itu dalam tatatanda kuasa tiga.
Penyelesaian:
(a)
$$ \begin{aligned} \text { Luas setiap permukaan kotak } & =2500 \mathrm{~mm}^2 \\ \text { Panjang } \times \text { Lebar } & =2500 \\ y \times y & =2500 \\ y^2 & =2500 \\ y & =\sqrt{2500} \\ & =\sqrt{50 \times 50} \\ & =50 \mathrm{~mm} \end{aligned} $$
(b)
$$ \begin{aligned} \text { Isi padu kotak hiasan } & =50 \mathrm{~mm} \times 50 \mathrm{~mm} \times 50 \mathrm{~mm} \\ & =(50 \mathrm{~mm})^3 \end{aligned} $$
Gambar foto di sebelah menunjukkan sebuah kotak hiasan yang berbentuk kubus. Setiap luas permukaan kotak itu ialah 2 500 mm2.
(a) Cari panjang tepi, dalam mm, kotak hiasan itu.
(b) Tulis isi padu kotak hiasan itu dalam tatatanda kuasa tiga.
Penyelesaian:
(a)
$$ \begin{aligned} \text { Luas setiap permukaan kotak } & =2500 \mathrm{~mm}^2 \\ \text { Panjang } \times \text { Lebar } & =2500 \\ y \times y & =2500 \\ y^2 & =2500 \\ y & =\sqrt{2500} \\ & =\sqrt{50 \times 50} \\ & =50 \mathrm{~mm} \end{aligned} $$
(b)
$$ \begin{aligned} \text { Isi padu kotak hiasan } & =50 \mathrm{~mm} \times 50 \mathrm{~mm} \times 50 \mathrm{~mm} \\ & =(50 \mathrm{~mm})^3 \end{aligned} $$
Soalan 7:
Cari nilai bagi setiap yang berikut.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{8}+(-0.3)^2 & =\sqrt[3]{2 \times 2 \times 2}+(-0.3)(-0.3) \\ & =2+0.09 \\ & =2.09 \end{aligned} $$
(b)
$$ \begin{aligned} 4^2 \times \sqrt[3]{-125} & =16 \times \sqrt[3]{(-5) \times(-5) \times(-5)} \\ & =16 \times(-5) \\ & =-80 \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt{36} \div\left(2 \frac{1}{2}\right)^2 & =\sqrt{6 \times 6} \div\left(\frac{5}{2}\right)^2 \\ & =6 \times \frac{4}{25} \\ & =\frac{24}{25} \end{aligned} $$
(d)
$$ \begin{aligned} & 3^2-\sqrt[3]{27} \div(-1)^3 \\ & =(3)(3)-\sqrt[3]{3 \times 3 \times 3} \div(-1)(-1)(-1) \\ & =9-[3 \div(-1)] \\ & =9-(-3) \\ & =9+3 \\ & =12 \end{aligned} $$
(e)
$$ \begin{aligned} & 5^2 \times \sqrt[3]{-216} \div \sqrt{\frac{4}{9}} \\ & =25 \times \sqrt[3]{(-6) \times(-6) \times(-6)} \div \frac{2}{3} \\ & =25 \times(-6) \times \frac{3}{2} \\ & =-225 \end{aligned} $$
(f)
$$ \begin{aligned} & \sqrt[3]{-\frac{1}{343}} \times\left(2^3-\sqrt{2 \frac{7}{9}}\right) \\ & =\sqrt[3]{-\frac{1}{7 \times 7 \times 7}} \times\left(8-\sqrt{\frac{25}{9}}\right) \\ & =-\frac{1}{7} \times\left(8-\frac{5}{3}\right) \\ & =-\frac{1}{7} \times\left(\frac{24}{3}-\frac{5}{3}\right) \\ & =-\frac{1}{7} \times \frac{19}{3} \\ & =-\frac{19}{21} \end{aligned} $$
Cari nilai bagi setiap yang berikut.
Penyelesaian:
(a)
$$ \begin{aligned} \sqrt[3]{8}+(-0.3)^2 & =\sqrt[3]{2 \times 2 \times 2}+(-0.3)(-0.3) \\ & =2+0.09 \\ & =2.09 \end{aligned} $$
(b)
$$ \begin{aligned} 4^2 \times \sqrt[3]{-125} & =16 \times \sqrt[3]{(-5) \times(-5) \times(-5)} \\ & =16 \times(-5) \\ & =-80 \end{aligned} $$
(c)
$$ \begin{aligned} \sqrt{36} \div\left(2 \frac{1}{2}\right)^2 & =\sqrt{6 \times 6} \div\left(\frac{5}{2}\right)^2 \\ & =6 \times \frac{4}{25} \\ & =\frac{24}{25} \end{aligned} $$
(d)
$$ \begin{aligned} & 3^2-\sqrt[3]{27} \div(-1)^3 \\ & =(3)(3)-\sqrt[3]{3 \times 3 \times 3} \div(-1)(-1)(-1) \\ & =9-[3 \div(-1)] \\ & =9-(-3) \\ & =9+3 \\ & =12 \end{aligned} $$
(e)
$$ \begin{aligned} & 5^2 \times \sqrt[3]{-216} \div \sqrt{\frac{4}{9}} \\ & =25 \times \sqrt[3]{(-6) \times(-6) \times(-6)} \div \frac{2}{3} \\ & =25 \times(-6) \times \frac{3}{2} \\ & =-225 \end{aligned} $$
(f)
$$ \begin{aligned} & \sqrt[3]{-\frac{1}{343}} \times\left(2^3-\sqrt{2 \frac{7}{9}}\right) \\ & =\sqrt[3]{-\frac{1}{7 \times 7 \times 7}} \times\left(8-\sqrt{\frac{25}{9}}\right) \\ & =-\frac{1}{7} \times\left(8-\frac{5}{3}\right) \\ & =-\frac{1}{7} \times\left(\frac{24}{3}-\frac{5}{3}\right) \\ & =-\frac{1}{7} \times \frac{19}{3} \\ & =-\frac{19}{21} \end{aligned} $$