Question

Find the value of √11 upto 3 decimal places by long division method

Answer 1

The value of √11 up to 3 decimal places is 3.316

Answer 2

√11 =3.316 correct upto three decimal places.

Given:

• $\sqrt{11}$

To find:

• Find the value upto 3- decimal places.

Solution:

Step 1:

Make pair of two digits from right to left.

Here, only two digits are present so put a decimal point, and zeros are taken in pairs.

$\: \: \: \: \: 3|11.00 \: \: 00 \: \: 00 \: \: | 3 \\ + 3|9| \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - \: \: \: \: \: \: \: \: \\ 6|2| \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Step 2:

Put decimal point in quotient and put two zeros after 2.

$\: \: \: \: \: 3|11.00 \: \: 00 \: \: 00 \: \: | 3.316 \\ + 3|9| \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - \: \: \: \: \: \: \: \: \\ 63|200| \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ + 3 |189| \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - \\ 661 |1100| \\ + 1 |661| \\ - - - - - - - \\ 6626 |43900| \\ + 6 |39756| \\ - - - - - - \\ |4144|$

Thus,

√11 is 3.316 correct upto three decimal places.

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