Solve sqrt{20/9*10^-3/1,5}

$$\sqrt { \frac { \frac { 20 } { 9 \times 10 ^ { - 3 } } } { 1,5 } }$$

Evaluate

$$\frac{200\sqrt{3}}{9}\approx 38.490017946$$

Solution Steps

Express \frac{\frac{20}{9\times 10^{-3}}}{1,5} as a single fraction.

$$\sqrt{\frac{20}{9\times 10^{-3}\times 1,5}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\sqrt{\frac{20}{9\times \frac{1}{1000}\times 1,5}}$$

Multiply 9 and \frac{1}{1000} to get \frac{9}{1000}.

$$\sqrt{\frac{20}{\frac{9}{1000}\times 1,5}}$$

Multiply \frac{9}{1000} and 1,5 to get \frac{27}{2000}.

$$\sqrt{\frac{20}{\frac{27}{2000}}}$$

Divide 20 by \frac{27}{2000} by multiplying 20 by the reciprocal of \frac{27}{2000}.

$$\sqrt{20\times \frac{2000}{27}}$$

Multiply 20 and \frac{2000}{27} to get \frac{40000}{27}.

$$\sqrt{\frac{40000}{27}}$$

Rewrite the square root of the division \sqrt{\frac{40000}{27}} as the division of square roots \frac{\sqrt{40000}}{\sqrt{27}}.

$$\frac{\sqrt{40000}}{\sqrt{27}}$$

Calculate the square root of 40000 and get 200.

$$\frac{200}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{200}{3\sqrt{3}}$$

Rationalize the denominator of \frac{200}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{200\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{200\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{200\sqrt{3}}{9}$$