Solve sqrt{4,5}:sqrt{2/9}

$$\sqrt { 4,5 } : \sqrt { \frac { 2 } { 9 } }$$

Evaluate

$$4,5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{9}} as the division of square roots \frac{\sqrt{2}}{\sqrt{9}}.

$$\frac{\sqrt{4,5}}{\frac{\sqrt{2}}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{4,5}}{\frac{\sqrt{2}}{3}}$$

Divide \sqrt{4,5} by \frac{\sqrt{2}}{3} by multiplying \sqrt{4,5} by the reciprocal of \frac{\sqrt{2}}{3}.

$$\frac{\sqrt{4,5}\times 3}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{4,5}\times 3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{4,5}\times 3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{4,5}\times 3\sqrt{2}}{2}$$

To multiply \sqrt{4,5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{9}\times 3}{2}$$

Calculate the square root of 9 and get 3.

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

Multiply 3 and 3 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$