Solve sqrt{4/91*5}

$$\sqrt{ \frac{ 4 }{ 9 } 1 \times 5 }$$

Evaluate

$$\frac{2\sqrt{5}}{3}\approx 1.490711985$$

Solution Steps

Multiply \frac{4}{9} and 1 to get \frac{4}{9}.

$$\sqrt{\frac{4}{9}\times 5}$$

Express \frac{4}{9}\times 5 as a single fraction.

$$\sqrt{\frac{4\times 5}{9}}$$

Multiply 4 and 5 to get 20.

$$\sqrt{\frac{20}{9}}$$

Rewrite the square root of the division \sqrt{\frac{20}{9}} as the division of square roots \frac{\sqrt{20}}{\sqrt{9}}.

$$\frac{\sqrt{20}}{\sqrt{9}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

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