Question

The square root of 2.9 up to two decimal places is:
A) 1.68
B) 1.70
C) 1.67
D) 1.71

Answer 1

Hint:We solve for the square root of the given number using the division method. Write the digits after the decimal in pair of two each starting from the right side and keep making pairs till all the digits are covered in the number ( digits before the decimal too). Then finding the suitable multiple of the term we divide the given number.

Complete step-by-step answer:
We expand the decimal number by writing three zeros after the number in decimal place.
The number \[2.9\]becomes \[2.9000\]
First we pair the digits in the number after the decimal point in pair of two each starting from the right side. Similarly we pair the digits before the decimal place.
\[2.9000 = \overline 2 .\overline {90} \overline {00} \]
Then we take the highest number whose square will be less than or equal to the first pair i.e. \[2\]
So, we know, \[1 \times 1 = 1,2 \times 2 = 4\]
We choose \[1 \times 1 = 1\] because \[1 < 2\]
Now we divide the number by taking this number as a divisor and taking the same number as quotient.
\[
  1\mathop{\left){\vphantom{1{\overline 2 .\overline {90} \overline {00} }}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{\overline 2 .\overline {90} \overline {00} }}}}
\limits^{\displaystyle \,\,\, 1} \\
   - 1 \\
  \overline { = 19000} \\
 \]
Now the remainder becomes the next dividend and the new divisor is twice the old divisor followed by a digit which makes a number such that the square of that number will be less than or equal to the new dividend. We place the decimal in the quotient and then write the next digit in the quotient.
So, we have a new dividend as \[19000\] and we can have a divisor as \[2 \times 1\underline {} = 2\underline {} \]where blank is filled by the same digit.
Now we try to find a number in the lane of twenties whose square is less than or equal to our new dividend.
\[
  21 \times 1 = 21 \\
  22 \times 2 = 44 \\
  23 \times 3 = 69 \\
  24 \times 4 = 96 \\
  25 \times 5 = 125 \\
  26 \times 6 = 156 \\
  27 \times 7 = 189 \\
  28 \times 8 = 224 \]
We can clearly see that \[27 \times 7 = 189\] suits our requirement because \[189 < 190\]
Now we divide the dividend by the number \[27\] and the quotient \[7\] comes after the decimal beside the earlier quotient.
\[
  27\mathop{\left){\vphantom{1{19000}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{19000}}}}
\limits^{\displaystyle \,\,\, {1.7}} \\
   - 18900 \\
  \overline { = 100} \\
 \]
So, we have a new dividend as \[100\] and we can have a divisor as \[2 \times 27\underline {} = 34\underline {} \] where blank is filled by the same digit.
Now we try to find a number in the lane of three hundred and forties whose square is less than or equal to our new dividend.
\[
  340 \times 0 = 0 \\
  341 \times 1 = 341\]
We can clearly see that \[340 \times 0 = 0\] suits our requirement because \[0 < 100\]
Now we divide the dividend by the number \[340\] and the quotient \[0\] comes beside the earlier quotient.
\[
  340\mathop{\left){\vphantom{1{100}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{100}}}}
\limits^{\displaystyle \,\,\, {1.70}} \\
   - 00 \\
  \overline { = 100}\]
So, we have quotient up to two decimal places.
Therefore, the square root of 2.9 is 1.70 up to two decimal places.

So, the correct answer is “Option B”.

Note:Students might make mistakes in finding the root up to two decimal places as they might not know that we can fix any number of zeros after the decimal and that will not change the value of the number. Also, when writing the division we need not write decimal in new dividends as it will just cause confusion.