Question

evaluate square root 2.8 up to three places of decimal​

Answer 1

Step-by-step explanation:

the answer is 1.673 because we have to find at three decimal place.

Answer 2

The square root of 2.8 up to three decimal places is 1.673

Given

√2.8

To Find

Square root up to 3 decimal places

Solution

First, we need to have even numbers before and after the decimal point.

Hence, we will take 2.8 as 2.80 to get

$\overline{|02 . 80}$

Now, we need to take the greatest number as the divisor that when squared is less than or equal to the pair of numbers before the decimal point, i.e 02.

Hence we get

$\hspace{0.25cm} 1\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\= 1$

Now we will bring the next pair of numbers down. Here it is 80. Since there is a decimal before it, our quotient will have the same.

$\hspace{0.25cm} 1\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\ \hspace{0.125 cm} \overline{| \hspace{0.125 cm}180}$

We will get the next divisor by multiplying the quotient by 2 and then taking the highest number with when multiplied by the divisor will be le than or equal to the dividend, i.e 180

Hence the number will be 6

Hence, we get the divisor as 26. we will now take 6 in the quotient line

$\hspace{0.25cm} 1.6\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\ \hspace{0.125 cm} 26\overline{| \hspace{0.125 cm}180}\\ -156\\= 24$

We will take 00 down to get a new dividend- 2400.

$\hspace{0.25cm} 1.6\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\ \hspace{0.125 cm} 26\overline{| \hspace{0.125 cm}180}\\ -156\\ \overline{ \hspace{0.25 cm}|2400}$

Now we will double 16 to get 32 as our new divisor. The other number will be 8, making the new divisor 268

$\hspace{0.25cm} 1.67\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\ \hspace{0.125 cm} \overline{26| \hspace{0.125 cm}180}\\ -156\\ 327\overline{ \hspace{0.025 cm}|2400}\\-2289\\\overline{=111}$

Now repeating the procedure as above we get

$\hspace{0.25cm} 1.673\\1 \overline{|02 . 80}\\\hspace{0.5cm} -1\\ \hspace{0.125 cm} \overline{26| \hspace{0.125 cm}180}\\ -156\\ 327\overline{ \hspace{0.025 cm}|2400}\\-2289\\\overline{3343|11100}\\{\hspace{0.5cm}-10029}\\\overline{\hspace{1cm}1071}$

Hence the square root of 2.8 up to three decimal places is 1.673

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