Solve sqrt{(-3)^2}*sqrt{27}*(-sqrt{3})+(-1/3)^-1+sqrt{2}*(-sqrt{10})+(-1^2012)

$$\sqrt { ( - 3 ) ^ { 2 } } \times \sqrt { 27 } \times ( - \sqrt { 3 } ) + ( - \frac { 1 } { 3 } ) ^ { - 1 } + \sqrt { 2 } \times ( - \sqrt { 10 } ) + ( - 1 ^ { 2012 } )$$

Evaluate

$$-2\sqrt{5}-31\approx -35.472135955$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\sqrt{9}\sqrt{27}\left(-\sqrt{3}\right)+\left(-\frac{1}{3}\right)^{-1}+\sqrt{2}\left(-\sqrt{10}\right)-1^{2012}$$

Calculate the square root of 9 and get 3.

$$3\sqrt{27}\left(-\sqrt{3}\right)+\left(-\frac{1}{3}\right)^{-1}+\sqrt{2}\left(-\sqrt{10}\right)-1^{2012}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\times 3\sqrt{3}\left(-\sqrt{3}\right)+\left(-\frac{1}{3}\right)^{-1}+\sqrt{2}\left(-\sqrt{10}\right)-1^{2012}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{3}\left(-\sqrt{3}\right)+\left(-\frac{1}{3}\right)^{-1}+\sqrt{2}\left(-\sqrt{10}\right)-1^{2012}$$

Calculate -\frac{1}{3} to the power of -1 and get -3.

$$9\sqrt{3}\left(-\sqrt{3}\right)-3+\sqrt{2}\left(-\sqrt{10}\right)-1^{2012}$$

Calculate 1 to the power of 2012 and get 1.

$$9\sqrt{3}\left(-\sqrt{3}\right)-3+\sqrt{2}\left(-\sqrt{10}\right)-1$$

Subtract 1 from -3 to get -4.

$$9\sqrt{3}\left(-\sqrt{3}\right)-4+\sqrt{2}\left(-\sqrt{10}\right)$$

Multiply 9 and -1 to get -9.

$$-9\sqrt{3}\sqrt{3}-4+\sqrt{2}\left(-1\right)\sqrt{10}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$-9\times 3-4+\sqrt{2}\left(-1\right)\sqrt{10}$$

Multiply -9 and 3 to get -27.

$$-27-4+\sqrt{2}\left(-1\right)\sqrt{10}$$

Subtract 4 from -27 to get -31.

$$-31+\sqrt{2}\left(-1\right)\sqrt{10}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$-31+\sqrt{2}\left(-1\right)\sqrt{2}\sqrt{5}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$-31+2\left(-1\right)\sqrt{5}$$

Multiply 2 and -1 to get -2.

$$-31-2\sqrt{5}$$