Solve 6*(-3)^-2+sqrt{8}+(1-2sqrt{2})-(sqrt{6}-3)^0

$$6 \cdot ( - 3 ) ^ { - 2 } + \sqrt { 8 } + ( 1 - 2 \sqrt { 2 } ) - ( \sqrt { 6 } - 3 ) ^ { 0 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$6\times \frac{1}{9}+\sqrt{8}+1-2\sqrt{2}-\left(\sqrt{6}-3\right)^{0}$$

Multiply 6 and \frac{1}{9} to get \frac{2}{3}.

$$\frac{2}{3}+\sqrt{8}+1-2\sqrt{2}-\left(\sqrt{6}-3\right)^{0}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2}{3}+2\sqrt{2}+1-2\sqrt{2}-\left(\sqrt{6}-3\right)^{0}$$

Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$\frac{5}{3}+2\sqrt{2}-2\sqrt{2}-\left(\sqrt{6}-3\right)^{0}$$

Combine 2\sqrt{2} and -2\sqrt{2} to get 0.

$$\frac{5}{3}-\left(\sqrt{6}-3\right)^{0}$$

Calculate \sqrt{6}-3 to the power of 0 and get 1.

$$\frac{5}{3}-1$$

Subtract 1 from \frac{5}{3} to get \frac{2}{3}.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$