Solve sqrt{90}div2sqrt{5}-sqrt{18}

$$\sqrt { 90 } \div 2 \sqrt { 5 } - \sqrt { 18 }$$

Evaluate

$$\frac{9\sqrt{2}}{2}\approx 6.363961031$$

Short Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{3\sqrt{10}}{2}\sqrt{5}-\sqrt{18}$$

Express \frac{3\sqrt{10}}{2}\sqrt{5} as a single fraction.

$$\frac{3\sqrt{10}\sqrt{5}}{2}-\sqrt{18}$$

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}.

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

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

$$\frac{3\sqrt{10}\sqrt{5}}{2}+\frac{2\left(-3\right)\sqrt{2}}{2}$$

Since \frac{3\sqrt{10}\sqrt{5}}{2} and \frac{2\left(-3\right)\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{10}\sqrt{5}+2\left(-3\right)\sqrt{2}}{2}$$

Do the multiplications in 3\sqrt{10}\sqrt{5}+2\left(-3\right)\sqrt{2}.

$$\frac{15\sqrt{2}-6\sqrt{2}}{2}$$

Do the calculations in 15\sqrt{2}-6\sqrt{2}.

$$\frac{9\sqrt{2}}{2}$$