Solve sqrt{75}*frac{sqrt{6}}{3}div1/sqrt{2}

$$\sqrt { 75 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$10$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}\times \frac{\sqrt{6}}{3}}{\frac{1}{\sqrt{2}}}$$

Express 5\times \frac{\sqrt{6}}{3} as a single fraction.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{1}{\sqrt{2}}}$$

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

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

Express \frac{5\sqrt{6}}{3}\sqrt{3} as a single fraction.

$$\frac{\frac{5\sqrt{6}\sqrt{3}}{3}}{\frac{\sqrt{2}}{2}}$$

Divide \frac{5\sqrt{6}\sqrt{3}}{3} by \frac{\sqrt{2}}{2} by multiplying \frac{5\sqrt{6}\sqrt{3}}{3} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}}$$

Rationalize the denominator of \frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\times 2}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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

Multiply 5 and 3 to get 15.

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

Multiply 15 and 2 to get 30.

$$\frac{30\sqrt{2}\sqrt{2}}{3\times 2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{30\times 2}{3\times 2}$$

Multiply 30 and 2 to get 60.

$$\frac{60}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{60}{6}$$

Divide 60 by 6 to get 10.

$$10$$

Factor

$$2\times 5$$