Solve sqrt{5}(sqrt{15}-sqrt{3/5})

$$\sqrt { 5 } ( \sqrt { 15 } - \sqrt { \frac { 3 } { 5 } } )$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Short Solution Steps

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

$$\sqrt{5}\left(\sqrt{15}-\frac{\sqrt{3}}{\sqrt{5}}\right)$$

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

$$\sqrt{5}\left(\sqrt{15}-\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)$$

The square of \sqrt{5} is 5.

$$\sqrt{5}\left(\sqrt{15}-\frac{\sqrt{3}\sqrt{5}}{5}\right)$$

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

$$\sqrt{5}\left(\sqrt{15}-\frac{\sqrt{15}}{5}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{15} times \frac{5}{5}.

$$\sqrt{5}\left(\frac{5\sqrt{15}}{5}-\frac{\sqrt{15}}{5}\right)$$

Since \frac{5\sqrt{15}}{5} and \frac{\sqrt{15}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{5}\times \frac{5\sqrt{15}-\sqrt{15}}{5}$$

Do the calculations in 5\sqrt{15}-\sqrt{15}.

$$\sqrt{5}\times \frac{4\sqrt{15}}{5}$$

Express \sqrt{5}\times \frac{4\sqrt{15}}{5} as a single fraction.

$$\frac{\sqrt{5}\times 4\sqrt{15}}{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{\sqrt{5}\times 4\sqrt{5}\sqrt{3}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\times 4\sqrt{3}}{5}$$

Multiply 5 and 4 to get 20.

$$\frac{20\sqrt{3}}{5}$$

Divide 20\sqrt{3} by 5 to get 4\sqrt{3}.

$$4\sqrt{3}$$