Solve frac{sqrt{75}}{sqrt{12}}+frac{sqrt{108}}{sqrt{147}}-sqrt{48}

$$\frac { \sqrt { 75 } } { \sqrt { 12 } } + \frac { \sqrt { 108 } } { \sqrt { 147 } } - \sqrt { 48 }$$

Evaluate

$$\frac{47}{14}-4\sqrt{3}\approx -3.571060373$$

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}.

$$\frac{5\sqrt{3}}{\sqrt{12}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

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}.

$$\frac{5\sqrt{3}}{2\sqrt{3}}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

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

$$\frac{5}{2}+\frac{\sqrt{108}}{\sqrt{147}}-\sqrt{48}$$

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}.

$$\frac{5}{2}+\frac{6\sqrt{3}}{\sqrt{147}}-\sqrt{48}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{5}{2}+\frac{6\sqrt{3}}{7\sqrt{3}}-\sqrt{48}$$

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

$$\frac{5}{2}+\frac{6}{7}-\sqrt{48}$$

Least common multiple of 2 and 7 is 14. Convert \frac{5}{2} and \frac{6}{7} to fractions with denominator 14.

$$\frac{35}{14}+\frac{12}{14}-\sqrt{48}$$

Since \frac{35}{14} and \frac{12}{14} have the same denominator, add them by adding their numerators.

$$\frac{35+12}{14}-\sqrt{48}$$

Add 35 and 12 to get 47.

$$\frac{47}{14}-\sqrt{48}$$

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}.

$$\frac{47}{14}-4\sqrt{3}$$