Solve 3sqrt{2}-sqrt{9/2}

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

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{2}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2}}.

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

Calculate the square root of 9 and get 3.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

$$\frac{6\sqrt{2}-3\sqrt{2}}{2}$$

Do the calculations in 6\sqrt{2}-3\sqrt{2}.

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