Solve 4/7sqrt{147}+3/8sqrt{192}-1/5sqrt{75}

$$\frac { 4 } { 7 } \sqrt { 147 } + \frac { 3 } { 8 } \sqrt { 192 } - \frac { 1 } { 5 } \sqrt { 75 }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

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}.

$$\frac{4}{7}\times 7\sqrt{3}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$$

Cancel out 7 and 7.

$$4\sqrt{3}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$4\sqrt{3}+\frac{3}{8}\times 8\sqrt{3}-\frac{1}{5}\sqrt{75}$$

Cancel out 8 and 8.

$$4\sqrt{3}+3\sqrt{3}-\frac{1}{5}\sqrt{75}$$

Combine 4\sqrt{3} and 3\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}-\frac{1}{5}\sqrt{75}$$

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}.

$$7\sqrt{3}-\frac{1}{5}\times 5\sqrt{3}$$

Cancel out 5 and 5.

$$7\sqrt{3}-\sqrt{3}$$

Combine 7\sqrt{3} and -\sqrt{3} to get 6\sqrt{3}.

$$6\sqrt{3}$$