Solve sqrt{450/461*560/567}

$$\sqrt { \frac { 450 } { 461 } \times \frac { 560 } { 567 } }$$

Evaluate

$$\frac{20\sqrt{4610}}{1383}\approx 0.981879693$$

Solution Steps

Reduce the fraction \frac{560}{567} to lowest terms by extracting and canceling out 7.

$$\sqrt{\frac{450}{461}\times \frac{80}{81}}$$

Multiply \frac{450}{461} times \frac{80}{81} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{450\times 80}{461\times 81}}$$

Do the multiplications in the fraction \frac{450\times 80}{461\times 81}.

$$\sqrt{\frac{36000}{37341}}$$

Reduce the fraction \frac{36000}{37341} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{4000}{4149}}$$

Rewrite the square root of the division \sqrt{\frac{4000}{4149}} as the division of square roots \frac{\sqrt{4000}}{\sqrt{4149}}.

$$\frac{\sqrt{4000}}{\sqrt{4149}}$$

Factor 4000=20^{2}\times 10. Rewrite the square root of the product \sqrt{20^{2}\times 10} as the product of square roots \sqrt{20^{2}}\sqrt{10}. Take the square root of 20^{2}.

$$\frac{20\sqrt{10}}{\sqrt{4149}}$$

Factor 4149=3^{2}\times 461. Rewrite the square root of the product \sqrt{3^{2}\times 461} as the product of square roots \sqrt{3^{2}}\sqrt{461}. Take the square root of 3^{2}.

$$\frac{20\sqrt{10}}{3\sqrt{461}}$$

Rationalize the denominator of \frac{20\sqrt{10}}{3\sqrt{461}} by multiplying numerator and denominator by \sqrt{461}.

$$\frac{20\sqrt{10}\sqrt{461}}{3\left(\sqrt{461}\right)^{2}}$$

The square of \sqrt{461} is 461.

$$\frac{20\sqrt{10}\sqrt{461}}{3\times 461}$$

To multiply \sqrt{10} and \sqrt{461}, multiply the numbers under the square root.

$$\frac{20\sqrt{4610}}{3\times 461}$$

Multiply 3 and 461 to get 1383.

$$\frac{20\sqrt{4610}}{1383}$$