Class 8: Cube Roots – Exercise 7E

Table of Cube Roots

2020-06-04_9-58-26

$\displaystyle \textbf{Question: }\text{Using the cube root table, find the values of:}$
$\displaystyle \text{(i) }\sqrt[3]{7}\qquad\text{(ii) }\sqrt[3]{30}\qquad \text{(iii) }\sqrt[3]{59}\qquad\text{(iv) }\sqrt[3]{110}$
$\displaystyle \text{(v) }\sqrt[3]{350}\qquad\text{(vi) }\sqrt[3]{4000}\qquad \text{(vii) }\sqrt[3]{490}\qquad\text{(viii) }\sqrt[3]{504}$
$\displaystyle \text{(ix) }\sqrt[3]{2214}\qquad\text{(x) }\sqrt[3]{2875}\qquad \text{(xi) }\sqrt[3]{734}\qquad\text{(xii) }\sqrt[3]{914}$

$\displaystyle \text{Answer:}$
$\displaystyle \text{(i) }\sqrt[3]{7}\approx1.913.$

$\displaystyle \text{(ii) }\sqrt[3]{30}=\sqrt[3]{3\times10}\approx3.107.$

$\displaystyle \text{(iii) }\sqrt[3]{59}\approx3.893.$

$\displaystyle \text{(iv) }\sqrt[3]{110}=\sqrt[3]{11\times10}\approx4.791.$

$\displaystyle \text{(v) }\sqrt[3]{350}=\sqrt[3]{35\times10}\approx7.047.$

$\displaystyle \text{(vi) }\sqrt[3]{4000} =\sqrt[3]{40\times100}\approx15.874.$

$\displaystyle \text{(vii) }\sqrt[3]{490} =\sqrt[3]{49\times10}\approx7.884.$

$\displaystyle \text{(viii) }\sqrt[3]{504} =\sqrt[3]{8\times63}=2\sqrt[3]{63}$
$\displaystyle \approx2\times3.979=7.958.$

$\displaystyle \text{(ix) }\sqrt[3]{2214} =\sqrt[3]{3^3\times82}=3\sqrt[3]{82}$
$\displaystyle \approx3\times4.344=13.032.$

$\displaystyle \text{(x) }\sqrt[3]{2875} =\sqrt[3]{5^3\times23}=5\sqrt[3]{23}$
$\displaystyle \approx5\times2.844=14.220.$

$\displaystyle \text{(xi) }\sqrt[3]{734}$
$\displaystyle \sqrt[3]{730}<\sqrt[3]{734}<\sqrt[3]{740}.$
$\displaystyle 9.004<\sqrt[3]{734}<9.045.$
$\displaystyle \text{For a difference of }10,\text{ the difference in cube-root values is}$
$\displaystyle 9.045-9.004=0.041.$
$\displaystyle \text{For a difference of }4,\text{ the corresponding difference is}$
$\displaystyle \frac{0.041\times4}{10}=0.0164.$
$\displaystyle \therefore \sqrt[3]{734}\approx9.004+0.0164=9.0204\approx9.020.$

$\displaystyle \text{(xii) }\sqrt[3]{914}$
$\displaystyle \sqrt[3]{910}<\sqrt[3]{914}<\sqrt[3]{920}.$
$\displaystyle \sqrt[3]{91\times10}<\sqrt[3]{914}<\sqrt[3]{92\times10}.$
$\displaystyle 9.691<\sqrt[3]{914}<9.726.$
$\displaystyle \text{For a difference of }10,\text{ the difference in values is}$
$\displaystyle 9.726-9.691=0.035.$
$\displaystyle \text{For a difference of }4,\text{ the difference in value is}$
$\displaystyle \frac{0.035\times4}{10}=0.014.$
$\displaystyle \therefore \sqrt[3]{914}\approx9.691+0.014=9.705.$
$\displaystyle \\$