sqrtfrac1212

The expression sqrtfrac1212 represents the square root of the fraction one hundred twenty-one over twelve. Mathematically, this can be written as $\sqrt{\frac{121}{12}}$.

To simplify this expression, we can first take the square root of the numerator and the denominator separately. The square root of 121 is 11, as $11 \times 11 = 121$. The square root of 12 can be simplified by factoring out perfect squares. Since $12 = 4 \times 3$, the square root of 12 is $\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$.

Therefore, $\sqrt{\frac{121}{12}} = \frac{\sqrt{121}}{\sqrt{12}} = \frac{11}{2\sqrt{3}}$.

It is common practice to rationalize the denominator, which means removing the square root from the denominator. To do this, we multiply both the numerator and the denominator by $\sqrt{3}$:

$\frac{11}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{11\sqrt{3}}{2 \times (\sqrt{3})^2} = \frac{11\sqrt{3}}{2 \times 3} = \frac{11\sqrt{3}}{6}$.

Thus, the simplified form of sqrtfrac1212 is $\frac{11\sqrt{3}}{6}$. This value is an irrational number, meaning it cannot be expressed as a simple fraction of two integers. Its approximate decimal value is 3.175.