Solve 3/4sqrt{176}-2/6sqrt{45}+1/8sqrt{320}+1/5sqrt{275}

$$\frac { 3 } { 4 } \sqrt { 176 } - \frac { 2 } { 6 } \sqrt { 45 } + \frac { 1 } { 8 } \sqrt { 320 } + \frac { 1 } { 5 } \sqrt { 275 }$$

Evaluate

$$4\sqrt{11}\approx 13.266499161$$

Solution Steps

Factor 176=4^{2}\times 11. Rewrite the square root of the product \sqrt{4^{2}\times 11} as the product of square roots \sqrt{4^{2}}\sqrt{11}. Take the square root of 4^{2}.

$$\frac{3}{4}\times 4\sqrt{11}-\frac{2}{6}\sqrt{45}+\frac{1}{8}\sqrt{320}+\frac{1}{5}\sqrt{275}$$

Cancel out 4 and 4.

$$3\sqrt{11}-\frac{2}{6}\sqrt{45}+\frac{1}{8}\sqrt{320}+\frac{1}{5}\sqrt{275}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$3\sqrt{11}-\frac{1}{3}\sqrt{45}+\frac{1}{8}\sqrt{320}+\frac{1}{5}\sqrt{275}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{11}-\frac{1}{3}\times 3\sqrt{5}+\frac{1}{8}\sqrt{320}+\frac{1}{5}\sqrt{275}$$

Cancel out 3 and 3.

$$3\sqrt{11}-\sqrt{5}+\frac{1}{8}\sqrt{320}+\frac{1}{5}\sqrt{275}$$

Factor 320=8^{2}\times 5. Rewrite the square root of the product \sqrt{8^{2}\times 5} as the product of square roots \sqrt{8^{2}}\sqrt{5}. Take the square root of 8^{2}.

$$3\sqrt{11}-\sqrt{5}+\frac{1}{8}\times 8\sqrt{5}+\frac{1}{5}\sqrt{275}$$

Cancel out 8 and 8.

$$3\sqrt{11}-\sqrt{5}+\sqrt{5}+\frac{1}{5}\sqrt{275}$$

Combine -\sqrt{5} and \sqrt{5} to get 0.

$$3\sqrt{11}+\frac{1}{5}\sqrt{275}$$

Factor 275=5^{2}\times 11. Rewrite the square root of the product \sqrt{5^{2}\times 11} as the product of square roots \sqrt{5^{2}}\sqrt{11}. Take the square root of 5^{2}.

$$3\sqrt{11}+\frac{1}{5}\times 5\sqrt{11}$$

Cancel out 5 and 5.

$$3\sqrt{11}+\sqrt{11}$$

Combine 3\sqrt{11} and \sqrt{11} to get 4\sqrt{11}.

$$4\sqrt{11}$$