Maths / Cube and Cube Roots / Cube Root by Prime Factorisation

QUESTION
 

Evaluate the following:

1.large 3sqrt{frac{0.027}{0.008}}div 3sqrt{frac{0.729}{0.512}}-frac{1}{3}
2.large 3sqrt{3343}+3sqrt{0.064}-3sqrt{0.125}
3.large left [left ( 3sqrt{frac{-216}{42875}}+3sqrt{frac{64}{125}}right ) right ]times 3sqrt{frac{343}{1331}}
OPTIONS
A. 

(i) - 1, (ii) - 6.9 , (iii) - 2/5

B. 

(i) - 3 , (ii) - 7.1 , (iii) - 1/5

C. 

(i) - 4 , (ii) - 7.9 , (iii) - 2/5

D. 

(i) - 1 , (ii) -  6.5 , (iii) - 1/5

Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

We have :

(i)3sqrt{frac{0.027}{0.008}}div 3sqrt{frac{0.729}{0.512}}-frac{1}{3}

= 3sqrt{frac{0.3times 0.3times 0.3}{0.2times 0.2times 0.2}}div 3sqrt{frac{0.9times 0.9 times 0.9}{0.8 times 0.8 times 0.8}}-frac{1}{3}

= left ( frac{0.3}{0.2} div frac{0.9}{0.8}right )-frac{1}{3}=left ( frac{0.3}{0.2}times frac{0.8}{0.9} right )-frac{1}{3}=frac{4}{3}-frac{1}{3}=1

We have,

(ii)3sqrt{3343}+3sqrt{0.064}-3sqrt{0.125}

= 3sqrt{7times 7 times 7}+3sqrt{0.4times 0.4times 0.4}-3sqrt{0.5times 0.5times 0.5}

= 7+0.4-0.5=7-0.1=6.9

We have

(iii)left [left ( 3sqrt{frac{-216}{42875}}+3sqrt{frac{64}{125}}right ) right ]times 3sqrt{frac{343}{1331}}

= left (frac{(-6)times (-6)times (-6)}{35times 35times 35} right ) ^{frac{1}{3}}+left ( frac{4times 4times 4}{5times 5times 5} right )^{frac{1}{3}}times left ( frac{7times 7times 7}{11times 11times 11} right )^{frac{1}{3}}

=left ( frac{-6}{35}+frac{4}{5} right )times left ( frac{7}{11} right )=left ( frac{-6div28}{35} right )times frac{7}{11}=frac{22}{35}times frac{7}{11}=frac{2}{5}

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