Table of Cube Roots Question: Using cube root table, find the values of:

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

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

(xi) $\sqrt{734}$    (xii) $\sqrt{914}$

Using cube root table, find the values of:

(i) $\sqrt{7}= 1.913$

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

(iii) $\sqrt{59 }=3.893$

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

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

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

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

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

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

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

(xi) $\sqrt{734}$ $\sqrt{730} < \sqrt{734} < \sqrt{740}$ $\sqrt{(73 \times 10)}< \sqrt{734}< \sqrt{(74 \times 10)}$ $9.004< \sqrt{734}< 9.045$

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 $\sqrt{734}=9.004+0.0164=9.0204$

(xii) $\sqrt{914}$ $\sqrt{910}< \sqrt{914}< \sqrt{920}$ $\sqrt{(91 \times 10)}< \sqrt{914}< \sqrt{(92 \times 10)}$ $9.691< \sqrt{914}< 9.726$

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 $\sqrt{914}=9.691+0.014=9.705$