Solve sqrt{12/3}*sqrt{27/10}

$$\sqrt { 1 \frac { 2 } { 3 } } \times \sqrt { \frac { 27 } { 10 } }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\sqrt{\frac{3+2}{3}}\sqrt{\frac{27}{10}}$$

Add 3 and 2 to get 5.

$$\sqrt{\frac{5}{3}}\sqrt{\frac{27}{10}}$$

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

$$\frac{\sqrt{5}}{\sqrt{3}}\sqrt{\frac{27}{10}}$$

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

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{\frac{27}{10}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}\sqrt{\frac{27}{10}}$$

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

$$\frac{\sqrt{15}}{3}\sqrt{\frac{27}{10}}$$

Rewrite the square root of the division \sqrt{\frac{27}{10}} as the division of square roots \frac{\sqrt{27}}{\sqrt{10}}.

$$\frac{\sqrt{15}}{3}\times \frac{\sqrt{27}}{\sqrt{10}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{3}}{\sqrt{10}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{3}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{3}\sqrt{10}}{10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{30}}{10}$$

Multiply \frac{\sqrt{15}}{3} times \frac{3\sqrt{30}}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{15}\times 3\sqrt{30}}{3\times 10}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{15}\sqrt{30}}{10}$$

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

$$\frac{\sqrt{15}\sqrt{15}\sqrt{2}}{10}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15\sqrt{2}}{10}$$

Divide 15\sqrt{2} by 10 to get \frac{3}{2}\sqrt{2}.

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