Solve sqrt{0.9*121/0.36*100}

$$\sqrt{ \frac{ 0.9 \cdot 121 }{ 0.36 \cdot 100 } }$$

Evaluate

$$\frac{11\sqrt{10}}{20}\approx 1.739252713$$

Solution Steps

Multiply 0.9 and 121 to get 108.9.

$$\sqrt{\frac{108.9}{0.36\times 100}}$$

Multiply 0.36 and 100 to get 36.

$$\sqrt{\frac{108.9}{36}}$$

Expand \frac{108.9}{36} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1089}{360}}$$

Reduce the fraction \frac{1089}{360} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{121}{40}}$$

Rewrite the square root of the division \sqrt{\frac{121}{40}} as the division of square roots \frac{\sqrt{121}}{\sqrt{40}}.

$$\frac{\sqrt{121}}{\sqrt{40}}$$

Calculate the square root of 121 and get 11.

$$\frac{11}{\sqrt{40}}$$

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}.

$$\frac{11}{2\sqrt{10}}$$

Rationalize the denominator of \frac{11}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{11\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{11\sqrt{10}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{11\sqrt{10}}{20}$$