Solve -sqrt{3/5}*sqrt{5/3}

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

Evaluate

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Solution Steps

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

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

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply -\frac{\sqrt{15}}{5} times \frac{\sqrt{15}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{15}\sqrt{15}}{5\times 3}$$

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

$$\frac{-15}{5\times 3}$$

Cancel out 3\times 5 in both numerator and denominator.

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Factor

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