Solve 6/82+sqrt{10/3}*sqrt{30/25}-sqrt{9}

$$\frac { 6 } { 8 } 2 + \sqrt { \frac { 10 } { 3 } } \cdot \sqrt { \frac { 30 } { 25 } } - \sqrt { 9 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}\times 2+\sqrt{\frac{10}{3}}\sqrt{\frac{30}{25}}-\sqrt{9}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{3\times 2}{4}+\sqrt{\frac{10}{3}}\sqrt{\frac{30}{25}}-\sqrt{9}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{4}+\sqrt{\frac{10}{3}}\sqrt{\frac{30}{25}}-\sqrt{9}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

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

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

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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

Calculate the square root of 9 and get 3.

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

Convert 3 to fraction \frac{6}{2}.

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

Since \frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from 3 to get -3.

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

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

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

Multiply 3 and 5 to get 15.

$$-\frac{3}{2}+\frac{30}{15}$$

Divide 30 by 15 to get 2.

$$-\frac{3}{2}+2$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{3}{2}+\frac{4}{2}$$

Since -\frac{3}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{-3+4}{2}$$

Add -3 and 4 to get 1.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$