Solve 2sqrt{10}-frac{sqrt{10}}{2}divsqrt{10}-frac{3sqrt{2}}{2}*sqrt{2}

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

Evaluate

$$2\sqrt{10}-\frac{7}{2}\approx 2.82455532$$

Solution Steps

Express \frac{\frac{\sqrt{10}}{2}}{\sqrt{10}} as a single fraction.

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

Rationalize the denominator of \frac{\sqrt{10}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$2\sqrt{10}-\frac{\sqrt{10}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}-\frac{3\sqrt{2}}{2}\sqrt{2}$$

The square of \sqrt{10} is 10.

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

Multiply \sqrt{10} and \sqrt{10} to get 10.

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

Multiply 2 and 10 to get 20.

$$2\sqrt{10}-\frac{10}{20}-\frac{3\sqrt{2}}{2}\sqrt{2}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$2\sqrt{10}-\frac{1}{2}-\frac{3\sqrt{2}}{2}\sqrt{2}$$

Express \frac{3\sqrt{2}}{2}\sqrt{2} as a single fraction.

$$2\sqrt{10}-\frac{1}{2}-\frac{3\sqrt{2}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{10}-\frac{1}{2}-\frac{3\times 2}{2}$$

Cancel out 2 and 2.

$$2\sqrt{10}-\frac{1}{2}-3$$

Convert 3 to fraction \frac{6}{2}.

$$2\sqrt{10}-\frac{1}{2}-\frac{6}{2}$$

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$2\sqrt{10}+\frac{-1-6}{2}$$

Subtract 6 from -1 to get -7.

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

Factor

$$\frac{4 \sqrt{10} - 7}{2} = 2.824555320336759$$