Solve frac{3sqrt{98}}{4}-frac{11sqrt{81}}{8}+frac{5sqrt{72}}{6}

$$\frac { 3 \sqrt { 98 } } { 4 } - \frac { 11 \sqrt { 81 } } { 8 } + \frac { 5 \sqrt { 72 } } { 6 }$$

Evaluate

$$\frac{41\sqrt{2}}{4}-\frac{99}{8}\approx 2.120689014$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{3\times 7\sqrt{2}}{4}-\frac{11\sqrt{81}}{8}+\frac{5\sqrt{72}}{6}$$

Multiply 3 and 7 to get 21.

$$\frac{21\sqrt{2}}{4}-\frac{11\sqrt{81}}{8}+\frac{5\sqrt{72}}{6}$$

Calculate the square root of 81 and get 9.

$$\frac{21\sqrt{2}}{4}-\frac{11\times 9}{8}+\frac{5\sqrt{72}}{6}$$

Multiply 11 and 9 to get 99.

$$\frac{21\sqrt{2}}{4}-\frac{99}{8}+\frac{5\sqrt{72}}{6}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{21\sqrt{2}}{4}-\frac{99}{8}+\frac{5\times 6\sqrt{2}}{6}$$

Multiply 5 and 6 to get 30.

$$\frac{21\sqrt{2}}{4}-\frac{99}{8}+\frac{30\sqrt{2}}{6}$$

Divide 30\sqrt{2} by 6 to get 5\sqrt{2}.

$$\frac{21\sqrt{2}}{4}-\frac{99}{8}+5\sqrt{2}$$

Combine \frac{21\sqrt{2}}{4} and 5\sqrt{2} to get \frac{41}{4}\sqrt{2}.

$$\frac{41}{4}\sqrt{2}-\frac{99}{8}$$

Factor

$$\frac{82 \sqrt{2} - 99}{8} = 2.120689014324226$$