Solve sqrt{3}*(3/5sqrt{7}-1/5sqrt{7})div2sqrt{7}=

$$\sqrt { 3 } \times ( \frac { 3 } { 5 } \sqrt { 7 } - \frac { 1 } { 5 } \sqrt { 7 } ) \div 2 \sqrt { 7 } =$$

Evaluate

$$\frac{7\sqrt{3}}{5}\approx 2.424871131$$

Solution Steps

Combine \frac{3}{5}\sqrt{7} and -\frac{1}{5}\sqrt{7} to get \frac{2}{5}\sqrt{7}.

$$\frac{\sqrt{3}\times \frac{2}{5}\sqrt{7}}{2}\sqrt{7}$$

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

$$\frac{\sqrt{21}\times \frac{2}{5}}{2}\sqrt{7}$$

Divide \sqrt{21}\times \frac{2}{5} by 2 to get \sqrt{21}\times \frac{1}{5}.

$$\sqrt{21}\times \frac{1}{5}\sqrt{7}$$

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$\sqrt{7}\sqrt{3}\times \frac{1}{5}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$7\times \frac{1}{5}\sqrt{3}$$

Multiply 7 and \frac{1}{5} to get \frac{7}{5}.

$$\frac{7}{5}\sqrt{3}$$