Solve sqrt{2*1.6*25/9}

$$\sqrt { \frac { 2 \times 1.6 \times 25 } { 9 } }$$

Evaluate

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

Solution Steps

Multiply 2 and 1.6 to get 3.2.

$$\sqrt{\frac{3.2\times 25}{9}}$$

Multiply 3.2 and 25 to get 80.

$$\sqrt{\frac{80}{9}}$$

Rewrite the square root of the division \sqrt{\frac{80}{9}} as the division of square roots \frac{\sqrt{80}}{\sqrt{9}}.

$$\frac{\sqrt{80}}{\sqrt{9}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

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

Calculate the square root of 9 and get 3.

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