Solve sqrt{0.00001331/81*90000}

$$\sqrt { \frac { 0.00001331 } { 81 } \times 90000 }$$

Evaluate

$$\frac{11\sqrt{11}}{300}\approx 0.121609576$$

Solution Steps

Expand \frac{0.00001331}{81} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{1331}{8100000000}\times 90000}$$

Express \frac{1331}{8100000000}\times 90000 as a single fraction.

$$\sqrt{\frac{1331\times 90000}{8100000000}}$$

Multiply 1331 and 90000 to get 119790000.

$$\sqrt{\frac{119790000}{8100000000}}$$

Reduce the fraction \frac{119790000}{8100000000} to lowest terms by extracting and canceling out 90000.

$$\sqrt{\frac{1331}{90000}}$$

Rewrite the square root of the division \sqrt{\frac{1331}{90000}} as the division of square roots \frac{\sqrt{1331}}{\sqrt{90000}}.

$$\frac{\sqrt{1331}}{\sqrt{90000}}$$

Factor 1331=11^{2}\times 11. Rewrite the square root of the product \sqrt{11^{2}\times 11} as the product of square roots \sqrt{11^{2}}\sqrt{11}. Take the square root of 11^{2}.

$$\frac{11\sqrt{11}}{\sqrt{90000}}$$

Calculate the square root of 90000 and get 300.

$$\frac{11\sqrt{11}}{300}$$