# Find the square root of 841 by division method?

Answer

Verified

280.2k+ views

**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.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is 1 divided by 0 class 8 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Convert compound sentence to simple sentence He is class 10 english CBSE

India lies between latitudes and longitudes class 12 social science CBSE

Why are rivers important for the countrys economy class 12 social science CBSE

Distinguish between Khadar and Bhangar class 9 social science CBSE