Solve 55/285*23sqrt{45*25}

$$5 \frac{ 5 }{ 285 \cdot 23 } \sqrt{ 45 \times 25 }$$

Evaluate

$$\frac{25\sqrt{5}}{437}\approx 0.127921509$$

Solution Steps

Multiply 285 and 23 to get 6555.

$$5\times \frac{5}{6555}\sqrt{45\times 25}$$

Reduce the fraction \frac{5}{6555} to lowest terms by extracting and canceling out 5.

$$5\times \frac{1}{1311}\sqrt{45\times 25}$$

Multiply 5 and \frac{1}{1311} to get \frac{5}{1311}.

$$\frac{5}{1311}\sqrt{45\times 25}$$

Multiply 45 and 25 to get 1125.

$$\frac{5}{1311}\sqrt{1125}$$

Factor 1125=15^{2}\times 5. Rewrite the square root of the product \sqrt{15^{2}\times 5} as the product of square roots \sqrt{15^{2}}\sqrt{5}. Take the square root of 15^{2}.

$$\frac{5}{1311}\times 15\sqrt{5}$$

Express \frac{5}{1311}\times 15 as a single fraction.

$$\frac{5\times 15}{1311}\sqrt{5}$$

Multiply 5 and 15 to get 75.

$$\frac{75}{1311}\sqrt{5}$$

Reduce the fraction \frac{75}{1311} to lowest terms by extracting and canceling out 3.

$$\frac{25}{437}\sqrt{5}$$