Solve 3sqrt{45}divsqrt{1/5}*2/3sqrt{3/3}

$$3 \sqrt { 45 } \div \sqrt { \frac { 1 } { 5 } } \times \frac { 2 } { 3 } \sqrt { \frac { 3 } { 3 } }$$

Evaluate

$$30$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{3\sqrt{45}}{\sqrt{\frac{1}{5}}}\times \frac{2}{3}\sqrt{1}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{5}}{\sqrt{\frac{1}{5}}}\times \frac{2}{3}\sqrt{1}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{9\sqrt{5}}{\frac{\sqrt{1}}{\sqrt{5}}}\times \frac{2}{3}\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$\frac{9\sqrt{5}}{\frac{1}{\sqrt{5}}}\times \frac{2}{3}\sqrt{1}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{9\sqrt{5}}{\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}\times \frac{2}{3}\sqrt{1}$$

The square of \sqrt{5} is 5.

$$\frac{9\sqrt{5}}{\frac{\sqrt{5}}{5}}\times \frac{2}{3}\sqrt{1}$$

Divide 9\sqrt{5} by \frac{\sqrt{5}}{5} by multiplying 9\sqrt{5} by the reciprocal of \frac{\sqrt{5}}{5}.

$$\frac{9\sqrt{5}\times 5}{\sqrt{5}}\times \frac{2}{3}\sqrt{1}$$

Rationalize the denominator of \frac{9\sqrt{5}\times 5}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{9\sqrt{5}\times 5\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{2}{3}\sqrt{1}$$

The square of \sqrt{5} is 5.

$$\frac{9\sqrt{5}\times 5\sqrt{5}}{5}\times \frac{2}{3}\sqrt{1}$$

Multiply 9 and 5 to get 45.

$$\frac{45\sqrt{5}\sqrt{5}}{5}\times \frac{2}{3}\sqrt{1}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{45\times 5}{5}\times \frac{2}{3}\sqrt{1}$$

Multiply 45 and 5 to get 225.

$$\frac{225}{5}\times \frac{2}{3}\sqrt{1}$$

Divide 225 by 5 to get 45.

$$45\times \frac{2}{3}\sqrt{1}$$

Express 45\times \frac{2}{3} as a single fraction.

$$\frac{45\times 2}{3}\sqrt{1}$$

Multiply 45 and 2 to get 90.

$$\frac{90}{3}\sqrt{1}$$

Divide 90 by 3 to get 30.

$$30\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$30\times 1$$

Multiply 30 and 1 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$