Solve 1115611sqrt{525/551}

$$1115611 \sqrt{ \frac{ 525 }{ 551 } }$$

Evaluate

$$\frac{5578055\sqrt{11571}}{551}\approx 1088971.816670138$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{525}{551}} as the division of square roots \frac{\sqrt{525}}{\sqrt{551}}.

$$1115611\times \frac{\sqrt{525}}{\sqrt{551}}$$

Factor 525=5^{2}\times 21. Rewrite the square root of the product \sqrt{5^{2}\times 21} as the product of square roots \sqrt{5^{2}}\sqrt{21}. Take the square root of 5^{2}.

$$1115611\times \frac{5\sqrt{21}}{\sqrt{551}}$$

Rationalize the denominator of \frac{5\sqrt{21}}{\sqrt{551}} by multiplying numerator and denominator by \sqrt{551}.

$$1115611\times \frac{5\sqrt{21}\sqrt{551}}{\left(\sqrt{551}\right)^{2}}$$

The square of \sqrt{551} is 551.

$$1115611\times \frac{5\sqrt{21}\sqrt{551}}{551}$$

To multiply \sqrt{21} and \sqrt{551}, multiply the numbers under the square root.

$$1115611\times \frac{5\sqrt{11571}}{551}$$

Express 1115611\times \frac{5\sqrt{11571}}{551} as a single fraction.

$$\frac{1115611\times 5\sqrt{11571}}{551}$$

Multiply 1115611 and 5 to get 5578055.

$$\frac{5578055\sqrt{11571}}{551}$$