Solve -3/2-1/sqrt{18}

$$\frac{ - \frac{ 3 }{ 2 } -1 }{ \sqrt{ 18 } }$$

Evaluate

$$-\frac{5\sqrt{2}}{12}\approx -0.589255651$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{-\frac{3}{2}-\frac{2}{2}}{\sqrt{18}}$$

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

$$\frac{\frac{-3-2}{2}}{\sqrt{18}}$$

Subtract 2 from -3 to get -5.

$$\frac{-\frac{5}{2}}{\sqrt{18}}$$

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}.

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

Express \frac{-\frac{5}{2}}{3\sqrt{2}} as a single fraction.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 3 to get 6.

$$\frac{-5\sqrt{2}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{-5\sqrt{2}}{12}$$