Question

Evaluate:
$\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}$
​

Answer 1

$\dag\:\underline{\sf AnsWer :}$

$:\implies \sf \sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}$

$:\implies \sf \sqrt[3]{3 \times 3 \times 3} + \sqrt[3]{ \dfrac{8}{1000} } + \sqrt[3]{ \dfrac{64}{1000} }$

$:\implies \sf 3 + \dfrac{\sqrt[3]{ 8}}{ \sqrt[3]{1000} } + \dfrac{\sqrt[3]{64}}{ \sqrt[3]{1000} }$

$:\implies \sf 3 + \dfrac{\sqrt[3]{2 \times 2 \times 2}}{ \sqrt[3]{10 \times 10 \times 10} } + \dfrac{\sqrt[3]{4 \times 4 \times 4}}{ \sqrt[3]{10 \times 10 \times 10} }$

$:\implies \sf 3 + \dfrac{2}{10} + \dfrac{4}{10}$

$:\implies \sf 3 + \dfrac{2 + 4}{10}$

$:\implies \sf 3 + \dfrac{6}{10}$

$:\implies \sf 10 \times 3 + \dfrac{6}{10}$

$:\implies \sf \dfrac{30 + 6}{10}$

$:\implies \sf \dfrac{36}{10}$

$:\implies \underline{ \boxed{ \sf 3.6 }}$

Answer 2

Correct Question-:

• $\dag{\sf{Evaluate:}}$
• $\boxed{\sf{\implies {\large{\purple{Expression \:=\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}\: }}}}}$

AnswEr-:

• $\boxed{\sf{\implies {\large{\pink{\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}\: = \: 3.6}}}}}$

EXPLANATION-:

• $\dag{\sf{Evaluate:}}$

• $\sf{\implies {\large{\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}}}}$

• $\sf{\implies {\large{\sqrt[3]{3×3×3} + \sqrt[3]{0.2×0.2×0.2} + \sqrt[3]{0.4×0.4×0.4}}}}$

• $\sf{\implies {\large{\sqrt[3]{3^{3}} + \sqrt[3]{0.2^{3}} + \sqrt[3]{0.4^{3}}}}}$

• $\dag{\sf{\large{We\:know\:that\: -:}}}$

• $\star{\sf{\large{\bf{\:\sqrt[a]{y^{a}} -:\:y}}}}$

• $\large{\sf{Now,\: -:}}$

• $\sf{\implies {\large{\sqrt[3]{3^{3}} + \sqrt[3]{0.2^{3}} + \sqrt[3]{0.4^{3}}}}}$ =

• $\sf{\implies {\large{ 3 + 0.2 + 0.4 }}}$

• $\sf{\implies {\large{ 3 + 0.6 }}}$

• $\sf{\implies {\large{ 3.6 }}}$

Hence ,

• $\boxed{\sf{\implies {\large{\pink{\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}\: = \: 3.6}}}}}$

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