Solve sqrt{10*3/4/1*frac{3{5}}}

$$\sqrt { \frac { 10 \times \frac { 3 } { 4 } } { 1 \times \frac { 3 } { 5 } } }$$

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

Solution Steps

Express 10\times \frac{3}{4} as a single fraction.

$$\sqrt{\frac{\frac{10\times 3}{4}}{1\times \frac{3}{5}}}$$

Multiply 10 and 3 to get 30.

$$\sqrt{\frac{\frac{30}{4}}{1\times \frac{3}{5}}}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{15}{2}}{1\times \frac{3}{5}}}$$

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

$$\sqrt{\frac{\frac{15}{2}}{\frac{3}{5}}}$$

Divide \frac{15}{2} by \frac{3}{5} by multiplying \frac{15}{2} by the reciprocal of \frac{3}{5}.

$$\sqrt{\frac{15}{2}\times \frac{5}{3}}$$

Multiply \frac{15}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{15\times 5}{2\times 3}}$$

Do the multiplications in the fraction \frac{15\times 5}{2\times 3}.

$$\sqrt{\frac{75}{6}}$$

Reduce the fraction \frac{75}{6} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{25}{2}}$$

Rewrite the square root of the division \sqrt{\frac{25}{2}} as the division of square roots \frac{\sqrt{25}}{\sqrt{2}}.

$$\frac{\sqrt{25}}{\sqrt{2}}$$

Calculate the square root of 25 and get 5.

$$\frac{5}{\sqrt{2}}$$

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

$$\frac{5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{2}}{2}$$