Solve 3/2sqrt{2}+1/3sqrt{8}-3/4sqrt{18}y

$$\frac{ 3 }{ 2 } \sqrt{ 2 } + \frac{ 1 }{ 3 } \sqrt{ 8 } - \frac{ 3 }{ 4 } \sqrt{ 18 } y$$

Evaluate

$$\frac{\sqrt{2}\left(26-27y\right)}{12}$$

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}.

$$\frac{3}{2}\sqrt{2}+\frac{1}{3}\times 2\sqrt{2}-\frac{3}{4}\sqrt{18}y$$

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

$$\frac{3}{2}\sqrt{2}+\frac{2}{3}\sqrt{2}-\frac{3}{4}\sqrt{18}y$$

Combine \frac{3}{2}\sqrt{2} and \frac{2}{3}\sqrt{2} to get \frac{13}{6}\sqrt{2}.

$$\frac{13}{6}\sqrt{2}-\frac{3}{4}\sqrt{18}y$$

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}.

$$\frac{13}{6}\sqrt{2}-\frac{3}{4}\times 3\sqrt{2}y$$

Express \frac{3}{4}\times 3 as a single fraction.

$$\frac{13}{6}\sqrt{2}-\frac{3\times 3}{4}\sqrt{2}y$$

Multiply 3 and 3 to get 9.

$$\frac{13}{6}\sqrt{2}-\frac{9}{4}\sqrt{2}y$$

Factor

$$\frac{\sqrt{2}\left(26-27y\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{18\sqrt{2}+8\sqrt{2}-27y\sqrt{2}}{12}$$