Solve sqrt{0.1*81/0.25*144}

$$\sqrt { \frac { 0.1 \times 81 } { 0.25 \times 144 } }$$

Evaluate

$$\frac{3\sqrt{10}}{20}\approx 0.474341649$$

Solution Steps

Cancel out 9 in both numerator and denominator.

$$\sqrt{\frac{0.1\times 9}{0.25\times 16}}$$

Multiply 0.1 and 9 to get 0.9.

$$\sqrt{\frac{0.9}{0.25\times 16}}$$

Multiply 0.25 and 16 to get 4.

$$\sqrt{\frac{0.9}{4}}$$

Expand \frac{0.9}{4} by multiplying both numerator and the denominator by 10.

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

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

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

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{40}}$$

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}.

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

Rationalize the denominator of \frac{3}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

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

Multiply 2 and 10 to get 20.

$$\frac{3\sqrt{10}}{20}$$