Solve sqrt{1/3}*(-sqrt{3})

$$\sqrt{ \frac{ 1 }{ 3 } } \times (- \sqrt{ 3 } )$$

Evaluate

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Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{1}}{\sqrt{3}}\left(-\sqrt{3}\right)$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}\left(-\sqrt{3}\right)$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express \frac{\sqrt{3}}{3}\left(-\sqrt{3}\right) as a single fraction.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-3}{3}$$

Cancel out 3 and 3.

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Factor

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