We are asked to find the square root of the mixed number $23 \frac{26}{121}$.

1. Problem Description

We are asked to find the square root of the mixed number $23 \frac{26}{121}$.

2. Solution Steps

First, we convert the mixed number to an improper fraction.

$23 \frac{26}{121} = \frac{23 \times 121 + 26}{121} = \frac{2783 + 26}{121} = \frac{2809}{121}$

Now, we take the square root of this improper fraction.

$\sqrt{23 \frac{26}{121}} = \sqrt{\frac{2809}{121}} = \frac{\sqrt{2809}}{\sqrt{121}}$

We need to find the square root of 2809 and

1

2

1. We know that $\sqrt{121}=11$.

Since $50^2 = 2500$ and $60^2 = 3600$, $\sqrt{2809}$ is between 50 and

6

0. Checking $53^2 = 53 \times 53 = 2809$, we have $\sqrt{2809} = 53$.

Thus, $\frac{\sqrt{2809}}{\sqrt{121}} = \frac{53}{11}$.

We can convert the improper fraction to a mixed number:

$\frac{53}{11} = 4 \frac{9}{11}$.

3. Final Answer

$\frac{53}{11}$ or $4 \frac{9}{11}$