Solve sqrt{1/3}*(2sqrt{12}-sqrt{75})

$$\sqrt{ \frac{ 1 }{ 3 } } \times (2 \sqrt{ 12 } - \sqrt{ 75 } )$$

Evaluate

$$-1$$

Solution Steps

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

$$\frac{\sqrt{1}}{\sqrt{3}}\left(2\sqrt{12}-\sqrt{75}\right)$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}\left(2\sqrt{12}-\sqrt{75}\right)$$

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

$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(2\sqrt{12}-\sqrt{75}\right)$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}\left(2\sqrt{12}-\sqrt{75}\right)$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\sqrt{3}}{3}\left(2\times 2\sqrt{3}-\sqrt{75}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{3}}{3}\left(4\sqrt{3}-\sqrt{75}\right)$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{\sqrt{3}}{3}\left(4\sqrt{3}-5\sqrt{3}\right)$$

Combine 4\sqrt{3} and -5\sqrt{3} to get -\sqrt{3}.

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

Express \frac{\sqrt{3}}{3}\sqrt{3} as a single fraction.

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

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

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

Divide 3 by 3 to get 1.

$$1\left(-1\right)$$

Multiply 1 and -1 to get -1.

$$-1$$

Factor

$$-1$$