Solve 2/3sqrt{3^2*2}+3/5sqrt{5^2*2}-1/3sqrt{3^2*5}=

$$\frac { 2 } { 3 } \sqrt { 3 ^ { 2 } \cdot 2 } + \frac { 3 } { 5 } \sqrt { 5 ^ { 2 } \cdot 2 } - \frac { 1 } { 3 } \sqrt { 3 ^ { 2 } \cdot 5 } =$$

Evaluate

$$\sqrt{5}\left(\sqrt{10}-1\right)\approx 4.834999834$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{3}\sqrt{9\times 2}+\frac{3}{5}\sqrt{5^{2}\times 2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Multiply 9 and 2 to get 18.

$$\frac{2}{3}\sqrt{18}+\frac{3}{5}\sqrt{5^{2}\times 2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

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}.

$$\frac{2}{3}\times 3\sqrt{2}+\frac{3}{5}\sqrt{5^{2}\times 2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Cancel out 3 and 3.

$$2\sqrt{2}+\frac{3}{5}\sqrt{5^{2}\times 2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Calculate 5 to the power of 2 and get 25.

$$2\sqrt{2}+\frac{3}{5}\sqrt{25\times 2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Multiply 25 and 2 to get 50.

$$2\sqrt{2}+\frac{3}{5}\sqrt{50}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{2}+\frac{3}{5}\times 5\sqrt{2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Cancel out 5 and 5.

$$2\sqrt{2}+3\sqrt{2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}-\frac{1}{3}\sqrt{3^{2}\times 5}$$

Calculate 3 to the power of 2 and get 9.

$$5\sqrt{2}-\frac{1}{3}\sqrt{9\times 5}$$

Multiply 9 and 5 to get 45.

$$5\sqrt{2}-\frac{1}{3}\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$5\sqrt{2}-\frac{1}{3}\times 3\sqrt{5}$$

Cancel out 3 and 3.

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

Factor

$$\sqrt{5} {(\sqrt{2} \sqrt{5} - 1)} = 4.834999834$$