Solve sqrt{63352222555/52655225556}

$$\sqrt{ \frac{ 63352222555 }{ 52655225556 } }$$

Evaluate

$$\frac{\sqrt{833956392026858903895}}{26327612778}\approx 1.096882706$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{63352222555}{52655225556}} as the division of square roots \frac{\sqrt{63352222555}}{\sqrt{52655225556}}.

$$\frac{\sqrt{63352222555}}{\sqrt{52655225556}}$$

Factor 52655225556=2^{2}\times 13163806389. Rewrite the square root of the product \sqrt{2^{2}\times 13163806389} as the product of square roots \sqrt{2^{2}}\sqrt{13163806389}. Take the square root of 2^{2}.

$$\frac{\sqrt{63352222555}}{2\sqrt{13163806389}}$$

Rationalize the denominator of \frac{\sqrt{63352222555}}{2\sqrt{13163806389}} by multiplying numerator and denominator by \sqrt{13163806389}.

$$\frac{\sqrt{63352222555}\sqrt{13163806389}}{2\left(\sqrt{13163806389}\right)^{2}}$$

The square of \sqrt{13163806389} is 13163806389.

$$\frac{\sqrt{63352222555}\sqrt{13163806389}}{2\times 13163806389}$$

To multiply \sqrt{63352222555} and \sqrt{13163806389}, multiply the numbers under the square root.

$$\frac{\sqrt{833956392026858903895}}{2\times 13163806389}$$

Multiply 2 and 13163806389 to get 26327612778.

$$\frac{\sqrt{833956392026858903895}}{26327612778}$$