Solve 22/245sqrt{558}

$$\frac{ 22 }{ 24 } 5 \sqrt{ 558 }$$

Evaluate

$$\frac{55\sqrt{62}}{4}\approx 108.267608268$$

Solution Steps

Reduce the fraction \frac{22}{24} to lowest terms by extracting and canceling out 2.

$$5\times \frac{11}{12}\sqrt{558}$$

Express 5\times \frac{11}{12} as a single fraction.

$$\frac{5\times 11}{12}\sqrt{558}$$

Multiply 5 and 11 to get 55.

$$\frac{55}{12}\sqrt{558}$$

Factor 558=3^{2}\times 62. Rewrite the square root of the product \sqrt{3^{2}\times 62} as the product of square roots \sqrt{3^{2}}\sqrt{62}. Take the square root of 3^{2}.

$$\frac{55}{12}\times 3\sqrt{62}$$

Express \frac{55}{12}\times 3 as a single fraction.

$$\frac{55\times 3}{12}\sqrt{62}$$

Multiply 55 and 3 to get 165.

$$\frac{165}{12}\sqrt{62}$$

Reduce the fraction \frac{165}{12} to lowest terms by extracting and canceling out 3.

$$\frac{55}{4}\sqrt{62}$$