Solve frac{4sqrt{27}-2sqrt{12}+7sqrt{48}}{2sqrt{12}}

$$\frac{ 4 \sqrt{ 27 } -2 \sqrt{ 12 } +7 \sqrt{ 48 } }{ 2 \sqrt{ 12 } }$$

Evaluate

$$9$$

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}.

$$\frac{4\times 3\sqrt{3}-2\sqrt{12}+7\sqrt{48}}{2\sqrt{12}}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{3}-2\sqrt{12}+7\sqrt{48}}{2\sqrt{12}}$$

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}.

$$\frac{12\sqrt{3}-2\times 2\sqrt{3}+7\sqrt{48}}{2\sqrt{12}}$$

Multiply -2 and 2 to get -4.

$$\frac{12\sqrt{3}-4\sqrt{3}+7\sqrt{48}}{2\sqrt{12}}$$

Combine 12\sqrt{3} and -4\sqrt{3} to get 8\sqrt{3}.

$$\frac{8\sqrt{3}+7\sqrt{48}}{2\sqrt{12}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{8\sqrt{3}+7\times 4\sqrt{3}}{2\sqrt{12}}$$

Multiply 7 and 4 to get 28.

$$\frac{8\sqrt{3}+28\sqrt{3}}{2\sqrt{12}}$$

Combine 8\sqrt{3} and 28\sqrt{3} to get 36\sqrt{3}.

$$\frac{36\sqrt{3}}{2\sqrt{12}}$$

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}.

$$\frac{36\sqrt{3}}{2\times 2\sqrt{3}}$$

Multiply 2 and 2 to get 4.

$$\frac{36\sqrt{3}}{4\sqrt{3}}$$

Cancel out 4\sqrt{3} in both numerator and denominator.

$$9$$

Factor

$$3^{2}$$