Solve frac{sqrt{75}-sqrt{108}+sqrt{27}}{3sqrt{12}}

$$\frac { \sqrt { 75 } - \sqrt { 108 } + \sqrt { 27 } } { 3 \sqrt { 12 } }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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}.

$$\frac{5\sqrt{3}-\sqrt{108}+\sqrt{27}}{3\sqrt{12}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{5\sqrt{3}-6\sqrt{3}+\sqrt{27}}{3\sqrt{12}}$$

Combine 5\sqrt{3} and -6\sqrt{3} to get -\sqrt{3}.

$$\frac{-\sqrt{3}+\sqrt{27}}{3\sqrt{12}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{-\sqrt{3}+3\sqrt{3}}{3\sqrt{12}}$$

Combine -\sqrt{3} and 3\sqrt{3} to get 2\sqrt{3}.

$$\frac{2\sqrt{3}}{3\sqrt{12}}$$

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}.

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

Multiply 3 and 2 to get 6.

$$\frac{2\sqrt{3}}{6\sqrt{3}}$$

Cancel out 2\sqrt{3} in both numerator and denominator.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$