Solve frac{-2*sqrt{27}+3*sqrt{3}+sqrt{75}*7}{sqrt{12}}

$$\frac { - 2 \cdot \sqrt { 27 } + 3 \cdot \sqrt { 3 } + \sqrt { 75 } \cdot 7 } { \sqrt { 12 } }$$

Evaluate

$$16$$

Solution Steps

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}.

$$\frac{-2\times 3\sqrt{3}+3\sqrt{3}+7\sqrt{75}}{\sqrt{12}}$$

Multiply -2 and 3 to get -6.

$$\frac{-6\sqrt{3}+3\sqrt{3}+7\sqrt{75}}{\sqrt{12}}$$

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

$$\frac{-3\sqrt{3}+7\sqrt{75}}{\sqrt{12}}$$

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}.

$$\frac{-3\sqrt{3}+7\times 5\sqrt{3}}{\sqrt{12}}$$

Multiply 7 and 5 to get 35.

$$\frac{-3\sqrt{3}+35\sqrt{3}}{\sqrt{12}}$$

Combine -3\sqrt{3} and 35\sqrt{3} to get 32\sqrt{3}.

$$\frac{32\sqrt{3}}{\sqrt{12}}$$

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}.

$$\frac{32\sqrt{3}}{2\sqrt{3}}$$

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

$$16$$

Factor

$$2^{4}$$