Solve sqrt{400/18*5}

$$\sqrt { \frac { 400 } { 18 \cdot 5 } }$$

Evaluate

$$\frac{2\sqrt{10}}{3}\approx 2.108185107$$

Solution Steps

Multiply 18 and 5 to get 90.

$$\sqrt{\frac{400}{90}}$$

Reduce the fraction \frac{400}{90} to lowest terms by extracting and canceling out 10.

$$\sqrt{\frac{40}{9}}$$

Rewrite the square root of the division \sqrt{\frac{40}{9}} as the division of square roots \frac{\sqrt{40}}{\sqrt{9}}.

$$\frac{\sqrt{40}}{\sqrt{9}}$$

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}.

$$\frac{2\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

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