Solve sqrt{2}div3sqrt{40}

$$\sqrt{ 2 } \div 3 \sqrt{ 40 }$$

Evaluate

$$\frac{4\sqrt{5}}{3}\approx 2.98142397$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

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

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

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

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

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

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}.

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{5}}{3}$$