Solve =sqrt{1723/1246*1445/1106*100}

$$= \sqrt { \frac { 1723 } { 1246 } \times \frac { 1445 } { 1106 } \times 100 }$$

Evaluate

$$\frac{85\sqrt{60572065}}{49217}\approx 13.441259867$$

Solution Steps

Multiply \frac{1723}{1246} times \frac{1445}{1106} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1723\times 1445}{1246\times 1106}\times 100}$$

Do the multiplications in the fraction \frac{1723\times 1445}{1246\times 1106}.

$$\sqrt{\frac{2489735}{1378076}\times 100}$$

Express \frac{2489735}{1378076}\times 100 as a single fraction.

$$\sqrt{\frac{2489735\times 100}{1378076}}$$

Multiply 2489735 and 100 to get 248973500.

$$\sqrt{\frac{248973500}{1378076}}$$

Reduce the fraction \frac{248973500}{1378076} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{62243375}{344519}}$$

Rewrite the square root of the division \sqrt{\frac{62243375}{344519}} as the division of square roots \frac{\sqrt{62243375}}{\sqrt{344519}}.

$$\frac{\sqrt{62243375}}{\sqrt{344519}}$$

Factor 62243375=85^{2}\times 8615. Rewrite the square root of the product \sqrt{85^{2}\times 8615} as the product of square roots \sqrt{85^{2}}\sqrt{8615}. Take the square root of 85^{2}.

$$\frac{85\sqrt{8615}}{\sqrt{344519}}$$

Factor 344519=7^{2}\times 7031. Rewrite the square root of the product \sqrt{7^{2}\times 7031} as the product of square roots \sqrt{7^{2}}\sqrt{7031}. Take the square root of 7^{2}.

$$\frac{85\sqrt{8615}}{7\sqrt{7031}}$$

Rationalize the denominator of \frac{85\sqrt{8615}}{7\sqrt{7031}} by multiplying numerator and denominator by \sqrt{7031}.

$$\frac{85\sqrt{8615}\sqrt{7031}}{7\left(\sqrt{7031}\right)^{2}}$$

The square of \sqrt{7031} is 7031.

$$\frac{85\sqrt{8615}\sqrt{7031}}{7\times 7031}$$

To multiply \sqrt{8615} and \sqrt{7031}, multiply the numbers under the square root.

$$\frac{85\sqrt{60572065}}{7\times 7031}$$

Multiply 7 and 7031 to get 49217.

$$\frac{85\sqrt{60572065}}{49217}$$