Question

State true or false:
The square root of 56 correct to three decimal places is 7.483.

Answer 1

Hint: Here we will use the long division method to find the square root.
If it matches then the given statement would be true otherwise it would be false.
Long division method is used to divide a large number (usually three digits or more) by a number having two or more digits.

Complete step-by-step answer: Since we have to find the root of 56 correct to three decimal places
Therefore we will write 56 in decimals as:-
 \[ \Rightarrow 56.000000\]
Now we will apply a long division method to find its square root.
Applying long division method we get:-
First we will place a bar over the pair of numbers starting from the unit place and also the decimals.
\[ \Rightarrow \overline {56} .\overline {00} \overline {00} \overline {00} \]
Now we will take the largest number as the divisor whose square is less than or equal to 56 then divide and write the quotient.
\[
  7\mathop{\left){\vphantom{1{\overline {56} .\overline {00} \overline {00} \overline {00} }}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{\overline {56} .\overline {00} \overline {00} \overline {00} }}}}
\limits^{\displaystyle \,\,\, {7.}} \\
   - 49 \\
   \cdots \cdots \cdots \cdots \\
  7 \\
   \cdots \cdots \cdots \cdots \\
 \]
Now we will bring down 00, which is under the bar, to the right side of the remainder and add a decimal with the quotient as there is a decimal in dividend and double the value of the quotient and enter it with blank space on the right side. Next, we have to select the largest digit for the unit place of the divisor such that the new number, when multiplied by the new digit at the unit's place, is equal to or less than 700.
\[
  144\mathop{\left){\vphantom{1{700}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{700}}}}
\limits^{\displaystyle \,\,\, 4} \\
  {\text{ }} - 576 \\
   \cdots \cdots \cdots \cdots \cdots \\
  {\text{ 124}} \\
   \cdots \cdots \cdots \cdots \\
 \]
Again bring down 00, which is under the bar, to the right side of the remainder and double the value of the quotient and enter it with blank space on the right side. Next, we have to select the largest digit for the unit place of the divisor such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than 12400.
\[
  1488\mathop{\left){\vphantom{1{12400}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{12400}}}}
\limits^{\displaystyle \,\,\, 8} \\
  {\text{ }} - 11904 \\
   \cdots \cdots \cdots \cdots \cdots \\
  {\text{ 496}} \\
   \cdots \cdots \cdots \cdots \\
 \]
Again bring down 00, which is under the bar, to the right side of the remainder and double the value of the quotient and enter it with blank space on the right side. Next, we have to select the largest digit for the unit place of the divisor such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than 496.
\[
  14963\mathop{\left){\vphantom{1{49600}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{49600}}}}
\limits^{\displaystyle \,\,\, 3} \\
  {\text{ }} - 44889 \\
   \cdots \cdots \cdots \cdots \cdots \\
  {\text{ 4711}} \\
   \cdots \cdots \cdots \cdots \cdots \\
 \]
Hence the final quotient is 7.483 correct to three decimal places
Therefore the square root of 56 correct to three decimal places is 7.483
Hence the statement, the square root of 56 correct to three decimal places is 7.483 is TRUE.

Note: The student may make mistakes while selecting the right quotient, so one should follow the steps of the long division method carefully and should continue the process until the remainder comes out to be zero.
Since in this question we had to calculate only till three decimal places hence it is not necessary to get the final remainder as zero and also 56 is not a perfect square therefore we would never get remainder as zero.