Question

Find the value of ∛729-∛27/∛512+∛343

Answer 1

9 - 3/8 + 7,

16 - 3/8,

(128-3)/8,

125/8

Answer 2

$\displaystyle \sf{ \frac{ \sqrt[3]{729} - \sqrt[3]{27} }{ \sqrt[3]{512} + \sqrt[3]{343} } } = \bf \: \frac{2}{5}$

Given :

$\displaystyle \sf{ \frac{ \sqrt[3]{729} - \sqrt[3]{27} }{ \sqrt[3]{512} + \sqrt[3]{343} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Calculate the value of ∛729 , ∛27 , ∛512 , ∛343

729 = 9 × 9 × 9 = 9³

∴ ∛729 = 9

27 = 3 × 3 × 3 = 3³

∴ ∛27 = 3

512 = 8 × 8 × 8 = 8³

∴ ∛512 = 8

343 = 7 × 7 × 7 = 7³

∴ ∛343 = 7

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ \frac{ \sqrt[3]{729} - \sqrt[3]{27} }{ \sqrt[3]{512} + \sqrt[3]{343} } }$

$\displaystyle \sf{ = \frac{9 - 3}{8 + 7} }$

$\displaystyle \sf{ = \frac{6}{15} }$

$\displaystyle \sf{ = \frac{2}{5} }$

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