Solve 45224852sqrt{252/frac{2663{2562}}}

$$45224852 \sqrt{ \frac{ 252 }{ \frac{ 2663 }{ 2562 } } }$$

Evaluate

$$\frac{1899443784\sqrt{974658}}{2663}\approx 704176299.918186426$$

Solution Steps

Divide 252 by \frac{2663}{2562} by multiplying 252 by the reciprocal of \frac{2663}{2562}.

$$45224852\sqrt{252\times \frac{2562}{2663}}$$

Express 252\times \frac{2562}{2663} as a single fraction.

$$45224852\sqrt{\frac{252\times 2562}{2663}}$$

Multiply 252 and 2562 to get 645624.

$$45224852\sqrt{\frac{645624}{2663}}$$

Rewrite the square root of the division \sqrt{\frac{645624}{2663}} as the division of square roots \frac{\sqrt{645624}}{\sqrt{2663}}.

$$45224852\times \frac{\sqrt{645624}}{\sqrt{2663}}$$

Factor 645624=42^{2}\times 366. Rewrite the square root of the product \sqrt{42^{2}\times 366} as the product of square roots \sqrt{42^{2}}\sqrt{366}. Take the square root of 42^{2}.

$$45224852\times \frac{42\sqrt{366}}{\sqrt{2663}}$$

Rationalize the denominator of \frac{42\sqrt{366}}{\sqrt{2663}} by multiplying numerator and denominator by \sqrt{2663}.

$$45224852\times \frac{42\sqrt{366}\sqrt{2663}}{\left(\sqrt{2663}\right)^{2}}$$

The square of \sqrt{2663} is 2663.

$$45224852\times \frac{42\sqrt{366}\sqrt{2663}}{2663}$$

To multiply \sqrt{366} and \sqrt{2663}, multiply the numbers under the square root.

$$45224852\times \frac{42\sqrt{974658}}{2663}$$

Express 45224852\times \frac{42\sqrt{974658}}{2663} as a single fraction.

$$\frac{45224852\times 42\sqrt{974658}}{2663}$$

Multiply 45224852 and 42 to get 1899443784.

$$\frac{1899443784\sqrt{974658}}{2663}$$