Solve frac{5sqrt{27}+2sqrt{48}-sqrt{12}}{sqrt{75}-sqrt{3}}

$$\frac{ 5 \sqrt{ 27 } +2 \sqrt{ 48 } - \sqrt{ 12 } }{ \sqrt{ 75 } - \sqrt{ 3 } }$$

Evaluate

$$\frac{21}{4}=5.25$$

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}.

$$\frac{5\times 3\sqrt{3}+2\sqrt{48}-\sqrt{12}}{\sqrt{75}-\sqrt{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{3}+2\sqrt{48}-\sqrt{12}}{\sqrt{75}-\sqrt{3}}$$

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}.

$$\frac{15\sqrt{3}+2\times 4\sqrt{3}-\sqrt{12}}{\sqrt{75}-\sqrt{3}}$$

Multiply 2 and 4 to get 8.

$$\frac{15\sqrt{3}+8\sqrt{3}-\sqrt{12}}{\sqrt{75}-\sqrt{3}}$$

Combine 15\sqrt{3} and 8\sqrt{3} to get 23\sqrt{3}.

$$\frac{23\sqrt{3}-\sqrt{12}}{\sqrt{75}-\sqrt{3}}$$

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}.

$$\frac{23\sqrt{3}-2\sqrt{3}}{\sqrt{75}-\sqrt{3}}$$

Combine 23\sqrt{3} and -2\sqrt{3} to get 21\sqrt{3}.

$$\frac{21\sqrt{3}}{\sqrt{75}-\sqrt{3}}$$

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}.

$$\frac{21\sqrt{3}}{5\sqrt{3}-\sqrt{3}}$$

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

$$\frac{21\sqrt{3}}{4\sqrt{3}}$$

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

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$