Solve sqrt{8}+1/3sqrt{18}-(sqrt{3})^2

$$\sqrt { 8 } + \frac { 1 } { 3 } \sqrt { 18 } - ( \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$3\left(\sqrt{2}-1\right)\approx 1.242640687$$

Solution Steps

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}.

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

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}.

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

Multiply \frac{1}{3} and 3 to get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Factor

$$3 {(\sqrt{2} - 1)} = 1.242640687$$