Solve (2)*sqrt{12/3}divsqrt{21/3}*sqrt{12/5}

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

Evaluate

$$2$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

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

Express 2\times \frac{\sqrt{15}}{3} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{\frac{2\sqrt{15}}{3}}{\sqrt{\frac{6+1}{3}}}\sqrt{\frac{1\times 5+2}{5}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{2\sqrt{15}}{3}}{\sqrt{\frac{7}{3}}}\sqrt{\frac{1\times 5+2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$\frac{\frac{2\sqrt{15}}{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{1\times 5+2}{5}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{2\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{1\times 5+2}{5}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{2\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{1\times 5+2}{5}}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{2\sqrt{15}}{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{1\times 5+2}{5}}$$

Divide \frac{2\sqrt{15}}{3} by \frac{\sqrt{21}}{3} by multiplying \frac{2\sqrt{15}}{3} by the reciprocal of \frac{\sqrt{21}}{3}.

$$\frac{2\sqrt{15}\times 3}{3\sqrt{21}}\sqrt{\frac{1\times 5+2}{5}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{15}}{\sqrt{21}}\sqrt{\frac{1\times 5+2}{5}}$$

Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{2\sqrt{15}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{1\times 5+2}{5}}$$

The square of \sqrt{21} is 21.

$$\frac{2\sqrt{15}\sqrt{21}}{21}\sqrt{\frac{1\times 5+2}{5}}$$

To multiply \sqrt{15} and \sqrt{21}, multiply the numbers under the square root.

$$\frac{2\sqrt{315}}{21}\sqrt{\frac{1\times 5+2}{5}}$$

Factor 315=3^{2}\times 35. Rewrite the square root of the product \sqrt{3^{2}\times 35} as the product of square roots \sqrt{3^{2}}\sqrt{35}. Take the square root of 3^{2}.

$$\frac{2\times 3\sqrt{35}}{21}\sqrt{\frac{1\times 5+2}{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{35}}{21}\sqrt{\frac{1\times 5+2}{5}}$$

Divide 6\sqrt{35} by 21 to get \frac{2}{7}\sqrt{35}.

$$\frac{2}{7}\sqrt{35}\sqrt{\frac{1\times 5+2}{5}}$$

Multiply 1 and 5 to get 5.

$$\frac{2}{7}\sqrt{35}\sqrt{\frac{5+2}{5}}$$

Add 5 and 2 to get 7.

$$\frac{2}{7}\sqrt{35}\sqrt{\frac{7}{5}}$$

Rewrite the square root of the division \sqrt{\frac{7}{5}} as the division of square roots \frac{\sqrt{7}}{\sqrt{5}}.

$$\frac{2}{7}\sqrt{35}\times \frac{\sqrt{7}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2}{7}\sqrt{35}\times \frac{\sqrt{35}}{5}$$

Multiply \frac{2}{7} times \frac{\sqrt{35}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\sqrt{35}}{7\times 5}\sqrt{35}$$

Multiply 7 and 5 to get 35.

$$\frac{2\sqrt{35}}{35}\sqrt{35}$$

Express \frac{2\sqrt{35}}{35}\sqrt{35} as a single fraction.

$$\frac{2\sqrt{35}\sqrt{35}}{35}$$

Multiply \sqrt{35} and \sqrt{35} to get 35.

$$\frac{2\times 35}{35}$$

Cancel out 35 and 35.

$$2$$

Factor

$$2$$