Calculating Square Root of Mixed Number $1\frac{11}{25}$

To find the square root of the mixed number $1\frac{11}{25}$, follow these steps:

Step 1: Convert Mixed Number to Improper Fraction

First, convert the mixed number $1\frac{11}{25}$ into an improper fraction. Multiply the whole number (1) by the denominator (25) and add the numerator (11). Keep the same denominator (25).

$1\frac{11}{25} = \frac{(1 \times 25) + 11}{25} = \frac{25 + 11}{25} = \frac{36}{25}$

Step 2: Calculate the Square Root

Now, calculate the square root of the improper fraction $\frac{36}{25}$. Use the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.

$ \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} $

Calculate the square root of the numerator (36) and the denominator (25):

• $\sqrt{36} = 6$
• $\sqrt{25} = 5$

So, the square root is:

$ \frac{6}{5} $

Step 3: Convert Back to Mixed Number

Finally, convert the improper fraction $\frac{6}{5}$ back to a mixed number. Divide the numerator (6) by the denominator (5).

$ \frac{6}{5} = 1 \text{ with a remainder of } 1 $

This gives the mixed number $1\frac{1}{5}$.

Final Answer

Therefore, the square root of $1\frac{11}{25}$ is $1\frac{1}{5}$.