Question

find the value of √11 upto 3 decimal places​

Answer 1

Answer:

The following steps to find the square root by long division method

1. Draw lines over pairs of digits from right to left.

2. Find the greatest number whose square is less than or equal to the digits in the first group.

3. Take this number as the divisor and quotient of the first group and find the remainder.

4. Move the digits from the second group besides the remainder to get the new dividend.

5. Double the first divisor and bring it down as the new divisor.

6. Complete the divisor and continue the division.

7. Put the decimal point in the square root as soon as the integral part is exhausted.

8. Repeat the process till the remainder becomes zero.

3.316

3

11

.

00

00

00

9

63

200

189

661

1100

661

6626

43900

39756

414400

11

= 3.316 (correct upto two decimal places)

Answer 2

$\large\underline{\sf{Solution-}}$

To evaluate

$\red{\rm :\longmapsto\: \sqrt{11}}$

Using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:3.316 \:\:}}}\\ {\underline{\sf{3}}}& {\sf{\:\:11.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 9 \:  \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{63}}}& {\sf{\:\: \: \: \: \: 200 \:  \:  \:  \:\:\:}} \\{\sf{}}& \underline{\sf{\:\:\: 189 \:  \: \:\:}} \\ {\underline{\sf{661}}}& {\sf{\:\: \: \: \: \: \: \: 1100  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \:661\:\:}} \\ {\underline{\sf{6626}}}& {\sf{\:\: \: \: \: \: \: \: 43900  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \:39756\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  4144\:\:}} \end{array}\end{gathered}\end{gathered}$

Thus,

$\red{\rm :\longmapsto\: \sqrt{11} = 3.316}$

Additional Information :-

Let's solve the same type of problem!!!

Question :- Evaluate the following :-

$\blue{\rm :\longmapsto\:(1). \: \: \sqrt{13}}$

Using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:3.605 \:\:}}}\\ {\underline{\sf{3}}}& {\sf{\:\:13.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: 9 \:  \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{66}}}& {\sf{\:\: \: \: \: \: 400 \:  \:  \:  \:\:\:}} \\{\sf{}}& \underline{\sf{\:\:\: 396 \:  \: \:\:}} \\ {\underline{\sf{7205}}}& {\sf{\:\: \: \: \: \: \: \: 40000  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \:36025\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  3975\:\:}} \end{array}\end{gathered}\end{gathered}$

Thus,

$\blue{\rm :\longmapsto\: \sqrt{13} = 3.605}$

$\red{\rm :\longmapsto\:(2). \: \: \sqrt{7}}$

Using Long Division Method, we have

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:2.645 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:7.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\:4 \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{46}}}& {\sf{\:\:300 \:  \:  \:  \:   \:\:}} \\{\sf{}}& \underline{\sf{\:\:276 \:  \: \:  \: \:\:}} \\ {\underline{\sf{524}}}& {\sf{\:\:2400  \:\:}} \\{\sf{}}& \underline{\sf{\:\:2096\:\:}} \\ {\underline{\sf{5285}}}& {\sf{\:\: \:  \: \:  \:  \:  \:  30400\:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \:  \:  \:  \: 26425\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \: \: 3975\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}\end{gathered}\end{gathered}$

Thus,

$\red{\rm :\longmapsto\: \sqrt{7} = 2.645}$