Solve sqrt{14826/13.6*9.649}

$$\sqrt { \frac { 14826 } { 13.6 \times 9.649 } }$$

Evaluate

$$\frac{50\sqrt{1215976629}}{164033}\approx 10.629219865$$

Solution Steps

Multiply 13.6 and 9.649 to get 131.2264.

$$\sqrt{\frac{14826}{131.2264}}$$

Expand \frac{14826}{131.2264} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{148260000}{1312264}}$$

Reduce the fraction \frac{148260000}{1312264} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{18532500}{164033}}$$

Rewrite the square root of the division \sqrt{\frac{18532500}{164033}} as the division of square roots \frac{\sqrt{18532500}}{\sqrt{164033}}.

$$\frac{\sqrt{18532500}}{\sqrt{164033}}$$

Factor 18532500=50^{2}\times 7413. Rewrite the square root of the product \sqrt{50^{2}\times 7413} as the product of square roots \sqrt{50^{2}}\sqrt{7413}. Take the square root of 50^{2}.

$$\frac{50\sqrt{7413}}{\sqrt{164033}}$$

Rationalize the denominator of \frac{50\sqrt{7413}}{\sqrt{164033}} by multiplying numerator and denominator by \sqrt{164033}.

$$\frac{50\sqrt{7413}\sqrt{164033}}{\left(\sqrt{164033}\right)^{2}}$$

The square of \sqrt{164033} is 164033.

$$\frac{50\sqrt{7413}\sqrt{164033}}{164033}$$

To multiply \sqrt{7413} and \sqrt{164033}, multiply the numbers under the square root.

$$\frac{50\sqrt{1215976629}}{164033}$$