Solve 17.3/sqrt{frac{2*2.45{9.8}}}=

$$\frac { 17.3 } { \sqrt { \frac { 2 \times 2.45 } { 9.8 } } } =$$

Evaluate

$$\frac{173\sqrt{2}}{10}\approx 24.465894629$$

Solution Steps

Multiply 2 and 2.45 to get 4.9.

$$\frac{17.3}{\sqrt{\frac{4.9}{9.8}}}$$

Expand \frac{4.9}{9.8} by multiplying both numerator and the denominator by 10.

$$\frac{17.3}{\sqrt{\frac{49}{98}}}$$

Reduce the fraction \frac{49}{98} to lowest terms by extracting and canceling out 49.

$$\frac{17.3}{\sqrt{\frac{1}{2}}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{17.3}{\frac{\sqrt{1}}{\sqrt{2}}}$$

Calculate the square root of 1 and get 1.

$$\frac{17.3}{\frac{1}{\sqrt{2}}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{17.3}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{17.3}{\frac{\sqrt{2}}{2}}$$

Divide 17.3 by \frac{\sqrt{2}}{2} by multiplying 17.3 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{17.3\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{17.3\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{17.3\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{17.3\times 2\sqrt{2}}{2}$$

Multiply 17.3 and 2 to get 34.6.

$$\frac{34.6\sqrt{2}}{2}$$

Divide 34.6\sqrt{2} by 2 to get 17.3\sqrt{2}.

$$17.3\sqrt{2}$$