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

1. Problem Description

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

2. Solution Steps

First, we convert the mixed number into an improper fraction:

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

$23 \times 121 = 2783$

$2783 + 26 = 2809$

So, $23\frac{26}{121} = \frac{2809}{121}$

Now, we take the square root of the fraction:

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

We can separate the square root of the numerator and denominator:

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

We know that $\sqrt{121} = 11$. We need to find the square root of

2

8

0

9.

Since $50^2 = 2500$ and $60^2 = 3600$, the square root is between 50 and

6

0. We can try 53: $53 \times 53 = 2809$.

Thus, $\sqrt{2809} = 53$.

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

3. Final Answer

$\frac{53}{11}$