Free Practice Questions for Cube-and-cube-root in Maths

$\sqrt[3]{(216)^{-3} \div(343)^{-2}}$
$=\sqrt[3]{\left(6^{3}\right)^{-3} \times \frac{1}{\left(7^{3}\right)^{-2}}}=\sqrt[3]{6^{-9} \times\left(7^{3}\right)^{2}}=\frac{7^{2}}{6^{3}}=\frac{49}{216}$

$\begin{aligned} \sqrt[3]{0.000216} &=\sqrt[3]{\frac{216}{1000000}}=\sqrt[3]{\frac{6 \times 6 \times 6}{100 \times 100 \times 100}} \\ &=\frac{6}{100}=0.06 \end{aligned}$

$\sqrt[3]{1.728}=\sqrt[3]{1.2 \times 1.2 \times 1.2}=1.2$

$\sqrt[3]{21+\sqrt{16}+\sqrt[3]{8}}=\sqrt[3]{21+4+2}=\sqrt[3]{27}=3$

$\begin{aligned} \sqrt[3]{\frac{512}{729}}+\sqrt[3]{\frac{8}{27}} &+\sqrt{\frac{25}{81}} \\ &=\frac{8}{9}+\frac{2}{3}+\frac{5}{9}=\frac{8+6+5}{9}=\frac{19}{9}=2 \frac{1}{9} \end{aligned}$

$\frac{432}{625}=\frac{3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 3}{5 \times 5 \times 5 \times 5}$
उपरोक्त से स्पष्ट है, कि $2 / 5$ से भाग करने पर संख्या पूर्ण घन बन जाएगी।

$\sqrt{16 \sqrt[3]{512 \times 8}}$
$=\sqrt{16 \sqrt[3]{8 \times 8 \times 8 \times 2 \times 2 \times 2}}=\sqrt{16 \times 8 \times 2}=16$

$\frac{\sqrt[3]{8}}{\sqrt{16}} \div \sqrt{\frac{100}{49}} \times \sqrt[3]{125}=\frac{2}{4} \times \frac{7}{10} \times 5=\frac{7}{4}$

$\begin{aligned} 2 \sqrt[3]{32}-3 \sqrt[3]{4}+\sqrt[3]{500} \\ &=4 \sqrt[3]{4}-3 \sqrt[3]{4}+5 \sqrt[3]{4}=6 \sqrt[3]{4} \end{aligned}$

$\begin{aligned} \sqrt[3]{5832} &=\sqrt[3]{2 \times 2 \times 2 \times 9 \times 9 \times 9} \\ &=2 \times 9=18 \end{aligned}$

$\begin{aligned} \sqrt[3]{2744} &=\sqrt[3]{2 \times 2 \times 2 \times 7 \times 7 \times 7} \\ &=2 \times 7=14 \end{aligned}$

$\because 972=6 \times 6 \times 3 \times 3 \times 3$
उपरोक्त से स्पष्ट है, कि यदि 972 को 6 से गुणा किया जाए, तो गुणनफल पूर्ण घन होगा।

$\sqrt[3]{5 \frac{104}{125}}=\sqrt[3]{\frac{729}{125}}=\frac{9}{5}=1 \frac{4}{5}$

$\sqrt[3]{\sqrt{0.000729}}=\sqrt[3]{0.027}=0.3$

$\begin{aligned} \sqrt[3]{0.000001} &=\sqrt[3]{\frac{1}{1000000}} \\ &=\sqrt[3]{\frac{1}{100 \times 100 \times 100}}=\frac{1}{100}=0.01 \end{aligned}$