Solve frac{3sqrt{2}}{2sqrt{5}}-3/2

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

Evaluate

$$\frac{3\left(\sqrt{10}-5\right)}{10}\approx -0.551316702$$

Short Solution Steps

Rationalize the denominator of \frac{3\sqrt{2}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

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

$$\frac{3\sqrt{10}}{2\times 5}-\frac{3}{2}$$

Multiply 2 and 5 to get 10.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2 is 10. Multiply \frac{3}{2} times \frac{5}{5}.

$$\frac{3\sqrt{10}}{10}-\frac{3\times 5}{10}$$

Since \frac{3\sqrt{10}}{10} and \frac{3\times 5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\sqrt{10}-3\times 5}{10}$$

Do the multiplications in 3\sqrt{10}-3\times 5.

$$\frac{3\sqrt{10}-15}{10}$$

Factor

$$\frac{3 {(\sqrt{10} - 5)}}{10} = -0.5513167019494862$$