Solve sqrt{3/16}*sqrt{3/9}

$$\sqrt { \frac { 3 } { 16 } } \cdot \sqrt { \frac { 3 } { 9 } }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{16}} as the division of square roots \frac{\sqrt{3}}{\sqrt{16}}.

$$\frac{\sqrt{3}}{\sqrt{16}}\sqrt{\frac{3}{9}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{3}}{4}\sqrt{\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\sqrt{3}}{4}\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{3}}{4}\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{3}}{4}\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{4}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{3}}{4} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{3}{12}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$