Table of Cube Roots

Question: Using cube root table, find the values of:

(i) $\sqrt[3]{7}$     (ii) $\sqrt[3]{30}$     (iii) $\sqrt[3]{59 }$     (vi) $\sqrt[3]{110}$      (v) $\sqrt[3]{350}$

(vi) $\sqrt[3]{4000}$     (vii) $\sqrt[3]{490}$      (viii) $\sqrt[3]{504}$      (ix) $\sqrt[3]{2214}$     (x) $\sqrt[3]{2875}$

(xi) $\sqrt[3]{734}$    (xii) $\sqrt[3]{914}$

Using cube root table, find the values of:

(i) $\sqrt[3]{7}= 1.913$

(ii) $\sqrt[3]{30} = \sqrt[3]{(3 \times 10)}=3.170$

(iii) $\sqrt[3]{59 }=3.893$

(vi) $\sqrt[3]{110} = \sqrt[3]{(11 \times 10)}=4.791$

(v) $\sqrt[3]{350} = \sqrt[3]{(35 \times 10)}=7.047$

(vi) $\sqrt[3]{4000} = \sqrt[3]{(40 \times 100)}= 15.874$

(vii) $\sqrt[3]{490} = \sqrt[3]{(49 \times 10)}=7.884$

(viii) $\sqrt[3]{504} = \sqrt[3]{(8 \times 63)} =2 \sqrt[3]{63} =2 \times 3.979=7.958$

(ix) $\sqrt[3]{2214} = \sqrt[3]{(2 \times 3 \times 3 \times 3 \times 41)} = 3 \sqrt[3]{82}=3 \times 4.344 = 13.032$

(x) $\sqrt[3]{2875}= \sqrt[3]{(5 \times 5 \times 5 \times 23)}=5 \sqrt[3]{23}=5 \times 2.844=14.22$

(xi) $\sqrt[3]{734}$

$\sqrt[3]{730} < \sqrt[3]{734} < \sqrt[3]{740}$

$\sqrt[3]{(73 \times 10)}< \sqrt[3]{734}< \sqrt[3]{(74 \times 10)}$

$9.004< \sqrt[3]{734}< 9.045$

For a difference of $10$, the difference in values $= 9.045 - 9.004 = 0.041$

For a difference of $4$, the difference in value $\displaystyle = \frac{(0.041 \times 4) }{ 10} = 0.0164$

Therefore $\sqrt[3]{734}=9.004+0.0164=9.0204$

(xii) $\sqrt[3]{914}$

$\sqrt[3]{910}< \sqrt[3]{914}< \sqrt[3]{920}$

$\sqrt[3]{(91 \times 10)}< \sqrt[3]{914}< \sqrt[3]{(92 \times 10)}$

$9.691< \sqrt[3]{914}< 9.726$

For a difference of $10$, the difference in values $= 9.726-9.691=0.035$

For a difference of $4$, the difference in value $\displaystyle = \frac{(0.035 \times 4) }{ 10} = 0.014$

Therefore $\sqrt[3]{914}=9.691+0.014=9.705$