Solve 258(sqrt{45*55/2000}

$$258( \sqrt{ \frac{ 45 \times 55 }{ 2000 } }$$

Evaluate

$$\frac{387\sqrt{55}}{10}\approx 287.006881451$$

Solution Steps

Multiply 45 and 55 to get 2475.

$$258\sqrt{\frac{2475}{2000}}$$

Reduce the fraction \frac{2475}{2000} to lowest terms by extracting and canceling out 25.

$$258\sqrt{\frac{99}{80}}$$

Rewrite the square root of the division \sqrt{\frac{99}{80}} as the division of square roots \frac{\sqrt{99}}{\sqrt{80}}.

$$258\times \frac{\sqrt{99}}{\sqrt{80}}$$

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$258\times \frac{3\sqrt{11}}{\sqrt{80}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$258\times \frac{3\sqrt{11}}{4\sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{11}}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$258\times \frac{3\sqrt{11}\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$258\times \frac{3\sqrt{11}\sqrt{5}}{4\times 5}$$

To multiply \sqrt{11} and \sqrt{5}, multiply the numbers under the square root.

$$258\times \frac{3\sqrt{55}}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$258\times \frac{3\sqrt{55}}{20}$$

Express 258\times \frac{3\sqrt{55}}{20} as a single fraction.

$$\frac{258\times 3\sqrt{55}}{20}$$

Multiply 258 and 3 to get 774.

$$\frac{774\sqrt{55}}{20}$$

Divide 774\sqrt{55} by 20 to get \frac{387}{10}\sqrt{55}.

$$\frac{387}{10}\sqrt{55}$$