Solve sqrt{18}-3/sqrt{2}+2sqrt{2}

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

Evaluate

$$\frac{7\sqrt{2}}{2}\approx 4.949747468$$

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}.

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

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

Combine \frac{3}{2}\sqrt{2} and 2\sqrt{2} to get \frac{7}{2}\sqrt{2}.

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