Solve 2/11sqrt{108^1*5/8}sqrt{147}

$$\frac { 2 } { 11 } \sqrt { 108 ^ { 1 } \times \frac { 5 } { 8 } } \sqrt { 147 }$$

Evaluate

$$\frac{63\sqrt{10}}{11}\approx 18.111226599$$

Solution Steps

Calculate 108 to the power of 1 and get 108.

$$\frac{2}{11}\sqrt{108\times \frac{5}{8}}\sqrt{147}$$

Express 108\times \frac{5}{8} as a single fraction.

$$\frac{2}{11}\sqrt{\frac{108\times 5}{8}}\sqrt{147}$$

Multiply 108 and 5 to get 540.

$$\frac{2}{11}\sqrt{\frac{540}{8}}\sqrt{147}$$

Reduce the fraction \frac{540}{8} to lowest terms by extracting and canceling out 4.

$$\frac{2}{11}\sqrt{\frac{135}{2}}\sqrt{147}$$

Rewrite the square root of the division \sqrt{\frac{135}{2}} as the division of square roots \frac{\sqrt{135}}{\sqrt{2}}.

$$\frac{2}{11}\times \frac{\sqrt{135}}{\sqrt{2}}\sqrt{147}$$

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$\frac{2}{11}\times \frac{3\sqrt{15}}{\sqrt{2}}\sqrt{147}$$

Rationalize the denominator of \frac{3\sqrt{15}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2}{11}\times \frac{3\sqrt{15}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{147}$$

The square of \sqrt{2} is 2.

$$\frac{2}{11}\times \frac{3\sqrt{15}\sqrt{2}}{2}\sqrt{147}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{2}{11}\times \frac{3\sqrt{30}}{2}\sqrt{147}$$

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}.

$$\frac{2}{11}\times \frac{3\sqrt{30}}{2}\times 7\sqrt{3}$$

Express \frac{2}{11}\times 7 as a single fraction.

$$\frac{2\times 7}{11}\times \frac{3\sqrt{30}}{2}\sqrt{3}$$

Multiply 2 and 7 to get 14.

$$\frac{14}{11}\times \frac{3\sqrt{30}}{2}\sqrt{3}$$

Multiply \frac{14}{11} times \frac{3\sqrt{30}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 3\sqrt{30}}{11\times 2}\sqrt{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 7\sqrt{30}}{11}\sqrt{3}$$

Express \frac{3\times 7\sqrt{30}}{11}\sqrt{3} as a single fraction.

$$\frac{3\times 7\sqrt{30}\sqrt{3}}{11}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{3\times 7\sqrt{3}\sqrt{10}\sqrt{3}}{11}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\times 7\times 3\sqrt{10}}{11}$$

Multiply 3 and 7 to get 21.

$$\frac{21\times 3\sqrt{10}}{11}$$

Multiply 21 and 3 to get 63.

$$\frac{63\sqrt{10}}{11}$$