Solve (20sqrt{10}+10sqrt{18}):2sqrt{2}=

$$( 20 \sqrt { 10 } + 10 \sqrt { 18 } ) : 2 \sqrt { 2 } =$$

Evaluate

$$20\sqrt{5}+30\approx 74.72135955$$

Solution Steps

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}.

$$\frac{20\sqrt{10}+10\times 3\sqrt{2}}{2}\sqrt{2}$$

Multiply 10 and 3 to get 30.

$$\frac{20\sqrt{10}+30\sqrt{2}}{2}\sqrt{2}$$

Express \frac{20\sqrt{10}+30\sqrt{2}}{2}\sqrt{2} as a single fraction.

$$\frac{\left(20\sqrt{10}+30\sqrt{2}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 20\sqrt{10}+30\sqrt{2} by \sqrt{2}.

$$\frac{20\sqrt{10}\sqrt{2}+30\left(\sqrt{2}\right)^{2}}{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{20\sqrt{2}\sqrt{5}\sqrt{2}+30\left(\sqrt{2}\right)^{2}}{2}$$

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

$$\frac{20\times 2\sqrt{5}+30\left(\sqrt{2}\right)^{2}}{2}$$

Multiply 20 and 2 to get 40.

$$\frac{40\sqrt{5}+30\left(\sqrt{2}\right)^{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{40\sqrt{5}+30\times 2}{2}$$

Multiply 30 and 2 to get 60.

$$\frac{40\sqrt{5}+60}{2}$$

Factor

$$10 {(2 \sqrt{5} + 3)} = 74.72135955$$