Solve sqrt{21/2}-3sqrt{28}

$$\sqrt { 2 \frac { 1 } { 2 } } - 3 \sqrt { 28 }$$

Evaluate

$$\frac{\sqrt{10}}{2}-6\sqrt{7}\approx -14.293369036$$

Short Solution Steps

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4+1}{2}}-3\sqrt{28}$$

Add 4 and 1 to get 5.

$$\sqrt{\frac{5}{2}}-3\sqrt{28}$$

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\sqrt{5}}{\sqrt{2}}-3\sqrt{28}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-3\sqrt{28}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{5}\sqrt{2}}{2}-3\sqrt{28}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{2}-3\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\sqrt{10}}{2}-3\times 2\sqrt{7}$$

Multiply -3 and 2 to get -6.

$$\frac{\sqrt{10}}{2}-6\sqrt{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -6\sqrt{7} times \frac{2}{2}.

$$\frac{\sqrt{10}}{2}+\frac{2\left(-6\right)\sqrt{7}}{2}$$

Since \frac{\sqrt{10}}{2} and \frac{2\left(-6\right)\sqrt{7}}{2} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{10}+2\left(-6\right)\sqrt{7}}{2}$$

Do the multiplications in \sqrt{10}+2\left(-6\right)\sqrt{7}.

$$\frac{\sqrt{10}-12\sqrt{7}}{2}$$