Solve sqrt{18}-sqrt{7/2}

$$\sqrt { 18 } - \sqrt { \frac { 7 } { 2 } }$$

Evaluate

$$-\frac{\sqrt{14}}{2}+3\sqrt{2}\approx 2.371811994$$

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}.

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

Rewrite the square root of the division \sqrt{\frac{7}{2}} as the division of square roots \frac{\sqrt{7}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\sqrt{2}-\frac{\sqrt{7}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$3\sqrt{2}-\frac{\sqrt{14}}{2}$$

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

$$\frac{2\times 3\sqrt{2}}{2}-\frac{\sqrt{14}}{2}$$

Since \frac{2\times 3\sqrt{2}}{2} and \frac{\sqrt{14}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3\sqrt{2}-\sqrt{14}}{2}$$

Do the multiplications in 2\times 3\sqrt{2}-\sqrt{14}.

$$\frac{6\sqrt{2}-\sqrt{14}}{2}$$