Question

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

Answer 1

The correct option is -3.

Therefore

`(2)/(3)* √(81) -\sqrt[3]{-27}-(4)/(3)* \sqrt[3]{729} = -3`

Explanation:

Evaluate:

`(2)/(3)* √(81) -\sqrt[3]{-27}-(4)/(3)* \sqrt[3]{729} = ?`

Solution:

We Know that Square root and Cube root is given by

`√(x* x)=x....................Square\ Rooting\\\\and\\\\\sqrt[3]{x* x* x}=x............ Cube\ Rooting`

Also

`\sqrt[3]{-x* -x* -x} =-x`

Therefore,

`√(81)=√(9* 9) =9\\\\\sqrt[3]{-27}=\sqrt[3]{-3* -3* -3}=-3\\\\\sqrt[3]{729}=\sqrt[3]{9* 9* 9}=9`

Substituting the values we get

`(2)/(3)* 9 -(-3)-(4)/(3)* 9\\\\2* 3+3-12\\\\9-12\\\\-3`

Therefore

`(2)/(3)* √(81) -\sqrt[3]{-27}-(4)/(3)* \sqrt[3]{729} = -3`