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**Hint:**We need to find the square root of 841 using the long division method. The long division method is used to divide large numbers into groups or parts. We start to solve the given question by finding the dividend and divisor to perform the division.

**Complete step-by-step solution:**

We are given a whole number and are asked to find out the square root of the number by the long division method.

We will be solving the given question stepwise using the rules to find the square root by the long division method.

According to our question, we need to find the square root of 841 using the division method.

Firstly, we group the digits in pairs starting from the unit’s place. Each pair is referred to as a period.

Following the same, the number 841 can be grouped into two periods.

$\Rightarrow {{1}^{st}}period=08$

$\Rightarrow {{2}^{nd}}period=41$

$\overline{\left){08\text{ 41}}\right.}$

Next, we take the number as quotient and divisor whose square of the number is less than or equal to ${{1}^{st}}$ period.

In our case,

$\Rightarrow {{1}^{st}}period=08$

We know that the value of ${{2}^{2}}=4$

From the above, we can say that the square of the number 2 is less than 8.

Following the same, we get,

$\Rightarrow divisor=2$

$\Rightarrow quotient=2$

We need to place the numbers 2 and 4 in the long division as follows,

$2\overset{2}{\overline{\left){\begin{align}

& 08\,\,41 \\

& 04

\end{align}}\right.}}$

Subtracting the product of divisor and quotient from the ${{1}^{st}}$ period, we get,

$\Rightarrow remainder=8-\left( 2\times 2 \right)$

Simplifying the above equation, we get,

$\Rightarrow remainder=8-4$

$\Rightarrow remainder=4$

The remainder through long division is shown as follows,

$2\overset{2}{\overline{\left){\begin{align}

& 08\,\,41 \\

& \underline{04 \,\,\,\,\,\,\,\,} \\

& \,\,\,4

\end{align}}\right.}}$

Appending the ${{2}^{nd}}$ period to the remainder, we get,

$\Rightarrow new\text{ }dividend=441$

Showing the same through long division, we get,

$2\overset{2}{\overline{\left){\begin{align}

& 08\,\,41 \\

& \underline{04 \,\,\,\,\,\,\,\,} \\

& \,\,\,\,441

\end{align}}\right.}}$

Now, we need to square the quotient

$\Rightarrow {{2}^{2}}=4$

We need to find a number such that

$\Rightarrow 4\_\times \_\le 441$

By the trial-and-error method, we find that the largest number satisfying the inequality is 9.

Substituting the value of 9 in the inequality, we get,

$\Rightarrow 49\times 9=441$

We need to place the numbers 9 and 441 in the long division as follows,

$2\overset{29}{\overline{\left){\begin{align}

& 841 \\

& 4 \\

\end{align}}\right.}} \\

49{\overline{\left){\begin{align}

& 441 \\

& 441

\end{align}}\right.}}$

Subtracting the number 441 from the new dividend, we get,

The long division is represented as follows,

$2\overset{29}{\overline{\left){\begin{align}

& 841 \\

& 4 \\

\end{align}}\right.}} \\

49{\overline{\left){\begin{align}

& 441 \\

& \underline{441} \\

& 0

\end{align}}\right.}}$

The value of the remainder is zero. Hence, the long division has been performed.

From the above,

**$\therefore$ The square root of 841 by division method is 29.**

**Note:**The given question is a direct concept-based question, and no trick or formula is required to solve it. We should be careful while performing arithmetic operations on the numbers to get precise results.

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