The problem asks to find the square root of the mixed number $75\frac{46}{49}$. We need to calculate $\sqrt{75\frac{46}{49}}$.

1. Problem Description

The problem asks to find the square root of the mixed number $75\frac{46}{49}$. We need to calculate $\sqrt{75\frac{46}{49}}$.

2. Solution Steps

First, convert the mixed number $75\frac{46}{49}$ to an improper fraction.

$$75\frac{46}{49} = \frac{75 \times 49 + 46}{49} = \frac{3675 + 46}{49} = \frac{3721}{49}$$

Now, take the square root of the improper fraction:

$$\sqrt{75\frac{46}{49}} = \sqrt{\frac{3721}{49}}$$

We can separate the square root of a fraction as the fraction of square roots:

$$\sqrt{\frac{3721}{49}} = \frac{\sqrt{3721}}{\sqrt{49}}$$

We know that $\sqrt{49} = 7$.

Now we need to find the square root of

3

7

2

1. We can recognize that $60^2=3600$, so it's slightly above

6

0. $61^2=3721$.

So, $\sqrt{3721} = 61$.

Therefore,

$$\frac{\sqrt{3721}}{\sqrt{49}} = \frac{61}{7}$$

We can convert this back to a mixed number.

$\frac{61}{7} = 8 \frac{5}{7}$ since $61 = 8 \times 7 + 5$.

3. Final Answer

$\frac{61}{7}$ or $8 \frac{5}{7}$