Evaluate- - 216- -343 -

The correct option is B 42 On prime factorising, we get, 216=6× 6× 6 =6^3 . 343=7× 7× 7 =7^3 .Then, 343 =( 7)^3 .Therefore ...

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Standard VIII

Mathematics

Cube Root of a Cube Number Using Estimation

Evaluate: √...

Question

Evaluate: $\sqrt[3]{216 \times (- 343)}$ .

21

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- 42

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Solution

The correct option is B $- 42$
On prime factorising, we get,
$216 = 6 \times 6 \times 6 - -------- -$ $= 6^{3}$ .
$343 = 7 \times 7 \times 7 - -------- -$ $= 7^{3}$ .
Then, $- 343$ $= (- 7)^{3}$ .

Therefore, value of $\sqrt[3]{216 \times (- 343)}$ is:
$\sqrt[3]{6^{3} \times (- 7)^{3}} = 6 \times (- 7) = - 42$ .
Therefore, option $B$ is correct.

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Similar questions

Q. Evaluate :
(i)

\sqrt[3]{\frac{- 125}{343}}

(ii)

\sqrt[3]{\frac{216}{729}}

Q. Show that

\sqrt[3]{216 \times (- 343)} = \sqrt[3]{216} \times \sqrt[3]{- 343}

Q. Evaluate

10 - 2 \frac{1}{3} \times 3 + 3 \frac{3}{4} \div 2 \frac{1}{2} = ?

Q. Evaluate :

{(\frac{3}{4})}^{0} \times 2 \frac{1}{4} - {(2 \frac{1}{4})}^{0} \times \frac{3}{4}

Evaluate :
$(i) \frac{2}{3} - \frac{4}{5} (i i) \frac{- 4}{9} - \frac{2}{- 3} (i i i) - 1 - \frac{4}{9} (i v) \frac{- 2}{7} - \frac{3}{- 14} (v) \frac{- 5}{18} - \frac{- 2}{9} (v i) \frac{5}{21} - \frac{- 13}{42}$

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Evaluate: 3√216×(−343).

The correct option is B −42On prime factorising, we get,216=6×6×6–––––––––– =63.343=7×7×7–––––––––– =73.Then, −343 =(−7)3.Therefore, value of 3√216×(−343) is:3√63×(−7)3=6×(−7)=−42.Therefore, option B is correct.

Evaluate: $\sqrt[3]{216 \times (- 343)}$ .