Solve sqrt{18}-sqrt{8/9}

$$\sqrt { 18 } - \sqrt { \frac { 8 } { 9 } }$$

Evaluate

$$\frac{7\sqrt{2}}{3}\approx 3.299831646$$

Short Solution Steps

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}.

$$3\sqrt{2}-\sqrt{\frac{8}{9}}$$

Rewrite the square root of the division \sqrt{\frac{8}{9}} as the division of square roots \frac{\sqrt{8}}{\sqrt{9}}.

$$3\sqrt{2}-\frac{\sqrt{8}}{\sqrt{9}}$$

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}.

$$3\sqrt{2}-\frac{2\sqrt{2}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3\sqrt{2} times \frac{3}{3}.

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

Since \frac{3\times 3\sqrt{2}}{3} and \frac{2\sqrt{2}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 3\sqrt{2}-2\sqrt{2}.

$$\frac{9\sqrt{2}-2\sqrt{2}}{3}$$

Do the calculations in 9\sqrt{2}-2\sqrt{2}.

$$\frac{7\sqrt{2}}{3}$$