Table of Cube Roots

2020-06-04_9-58-26

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}

Answer:

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