Question

Evaluate 2/3 √81- 3^√-27 -4/33^√729
-9
3
-3

Answer 1

Answer:

The correct option is -3.

Therefore

$\dfrac{2}{3}\times \sqrt{81} -\sqrt[3]{-27}-\dfrac{4}{3}\times \sqrt[3]{729} = -3$

Step-by-step explanation:

Evaluate:

$\dfrac{2}{3}\times \sqrt{81} -\sqrt[3]{-27}-\dfrac{4}{3}\times \sqrt[3]{729} = ?$

Solution:

We Know that Square root and  Cube root is given by

$\sqrt{x\times x}=x....................Square\ Rooting\\\\and\\\\\sqrt[3]{x\times x\times x}=x............ Cube\ Rooting$

Also

$\sqrt[3]{-x\times -x\times -x} =-x$

Therefore,

$\sqrt{81}=\sqrt{9\times 9} =9\\\\\sqrt[3]{-27}=\sqrt[3]{-3\times -3\times -3}=-3\\\\\sqrt[3]{729}=\sqrt[3]{9\times 9\times 9}=9$

Substituting the values we get

$\dfrac{2}{3}\times 9 -(-3)-\dfrac{4}{3}\times 9\\\\2\times 3+3-12\\\\9-12\\\\-3$

Therefore

$\dfrac{2}{3}\times \sqrt{81} -\sqrt[3]{-27}-\dfrac{4}{3}\times \sqrt[3]{729} = -3$