Solve (1/3)^-1-(sqrt{5}-2)^0+sqrt{18}-(-2)^2*sqrt{2}

$$( \frac { 1 } { 3 } ) ^ { - 1 } - ( \sqrt { 5 } - 2 ) ^ { 0 } + \sqrt { 18 } - ( - 2 ) ^ { 2 } \times \sqrt { 2 }$$

Evaluate

$$2-\sqrt{2}\approx 0.585786438$$

Solution Steps

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

$$3-\left(\sqrt{5}-2\right)^{0}+\sqrt{18}-\left(-2\right)^{2}\sqrt{2}$$

Calculate \sqrt{5}-2 to the power of 0 and get 1.

$$3-1+\sqrt{18}-\left(-2\right)^{2}\sqrt{2}$$

Subtract 1 from 3 to get 2.

$$2+\sqrt{18}-\left(-2\right)^{2}\sqrt{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2+3\sqrt{2}-\left(-2\right)^{2}\sqrt{2}$$

Calculate -2 to the power of 2 and get 4.

$$2+3\sqrt{2}-4\sqrt{2}$$

Combine 3\sqrt{2} and -4\sqrt{2} to get -\sqrt{2}.

$$2-\sqrt{2}$$