Solve 585sqrt{822/44}

$$585 \sqrt{ \frac{ 822 }{ 44 } }$$

Evaluate

$$\frac{585\sqrt{9042}}{22}\approx 2528.514430901$$

Solution Steps

Reduce the fraction \frac{822}{44} to lowest terms by extracting and canceling out 2.

$$585\sqrt{\frac{411}{22}}$$

Rewrite the square root of the division \sqrt{\frac{411}{22}} as the division of square roots \frac{\sqrt{411}}{\sqrt{22}}.

$$585\times \frac{\sqrt{411}}{\sqrt{22}}$$

Rationalize the denominator of \frac{\sqrt{411}}{\sqrt{22}} by multiplying numerator and denominator by \sqrt{22}.

$$585\times \frac{\sqrt{411}\sqrt{22}}{\left(\sqrt{22}\right)^{2}}$$

The square of \sqrt{22} is 22.

$$585\times \frac{\sqrt{411}\sqrt{22}}{22}$$

To multiply \sqrt{411} and \sqrt{22}, multiply the numbers under the square root.

$$585\times \frac{\sqrt{9042}}{22}$$

Express 585\times \frac{\sqrt{9042}}{22} as a single fraction.

$$\frac{585\sqrt{9042}}{22}$$