Solve 52sqrt{5255/224}

$$52 \sqrt{ \frac{ 5255 }{ 224 } }$$

Evaluate

$$\frac{13\sqrt{73570}}{14}\approx 251.863767031$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5255}{224}} as the division of square roots \frac{\sqrt{5255}}{\sqrt{224}}.

$$52\times \frac{\sqrt{5255}}{\sqrt{224}}$$

Factor 224=4^{2}\times 14. Rewrite the square root of the product \sqrt{4^{2}\times 14} as the product of square roots \sqrt{4^{2}}\sqrt{14}. Take the square root of 4^{2}.

$$52\times \frac{\sqrt{5255}}{4\sqrt{14}}$$

Rationalize the denominator of \frac{\sqrt{5255}}{4\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$52\times \frac{\sqrt{5255}\sqrt{14}}{4\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$52\times \frac{\sqrt{5255}\sqrt{14}}{4\times 14}$$

To multiply \sqrt{5255} and \sqrt{14}, multiply the numbers under the square root.

$$52\times \frac{\sqrt{73570}}{4\times 14}$$

Multiply 4 and 14 to get 56.

$$52\times \frac{\sqrt{73570}}{56}$$

Express 52\times \frac{\sqrt{73570}}{56} as a single fraction.

$$\frac{52\sqrt{73570}}{56}$$

Divide 52\sqrt{73570} by 56 to get \frac{13}{14}\sqrt{73570}.

$$\frac{13}{14}\sqrt{73570}$$