Solve 2+sqrt{10/3}*sqrt{30/25}-sqrt{9}

$$2 + \sqrt { \frac { 10 } { 3 } } \cdot \sqrt { \frac { 30 } { 25 } } - \sqrt { 9 }$$

Evaluate

$$1$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{10}{3}} as the division of square roots \frac{\sqrt{10}}{\sqrt{3}}.

$$2+\frac{\sqrt{10}}{\sqrt{3}}\sqrt{\frac{30}{25}}-\sqrt{9}$$

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

$$2+\frac{\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{\frac{30}{25}}-\sqrt{9}$$

The square of \sqrt{3} is 3.

$$2+\frac{\sqrt{10}\sqrt{3}}{3}\sqrt{\frac{30}{25}}-\sqrt{9}$$

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

$$2+\frac{\sqrt{30}}{3}\sqrt{\frac{30}{25}}-\sqrt{9}$$

Reduce the fraction \frac{30}{25} to lowest terms by extracting and canceling out 5.

$$2+\frac{\sqrt{30}}{3}\sqrt{\frac{6}{5}}-\sqrt{9}$$

Rewrite the square root of the division \sqrt{\frac{6}{5}} as the division of square roots \frac{\sqrt{6}}{\sqrt{5}}.

$$2+\frac{\sqrt{30}}{3}\times \frac{\sqrt{6}}{\sqrt{5}}-\sqrt{9}$$

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

$$2+\frac{\sqrt{30}}{3}\times \frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\sqrt{9}$$

The square of \sqrt{5} is 5.

$$2+\frac{\sqrt{30}}{3}\times \frac{\sqrt{6}\sqrt{5}}{5}-\sqrt{9}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$2+\frac{\sqrt{30}}{3}\times \frac{\sqrt{30}}{5}-\sqrt{9}$$

Multiply \frac{\sqrt{30}}{3} times \frac{\sqrt{30}}{5} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{\sqrt{30}\sqrt{30}}{3\times 5}-\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$2+\frac{\sqrt{30}\sqrt{30}}{3\times 5}-3$$

Subtract 3 from 2 to get -1.

$$-1+\frac{\sqrt{30}\sqrt{30}}{3\times 5}$$

Multiply \sqrt{30} and \sqrt{30} to get 30.

$$-1+\frac{30}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$-1+\frac{30}{15}$$

Divide 30 by 15 to get 2.

$$-1+2$$

Add -1 and 2 to get 1.

$$1$$

Factor

$$1$$