Question

Find the square root of 2.89 using a long division method.

Answer 1

Hint: A square root of a number is a value that, when multiplied by itself, gives the number. Recall the method to find the square root by long division and find the value of the square root of 2.89.

Complete step-by-step answer:
The square root of a number is another number that produces the first number when it is multiplied by itself. For example, the square root of 25 is 5 because 5 multiplied with 5 is 25.
Sometimes, it is obvious to find the square root of a number, usually a smaller number but other times, the number might be big or decimal and we need to use a method called long division to arrive at the answer.

In this problem, we need to find the square root of 2.89.

As the first step in long division, we need to pair the digits from the right.

Hence, we pair 8 and 9 as 89, and the digit 2 has no digit to pair with.

\[{\text{2 }}{\text{. 89}}\]

Next, we need to find the largest integer such that its square is less than the first digit.

We know that \[{1^2}\] which is 1 is less than 2.

\[\begin{gathered}

  1\mathop{\left){\vphantom{1{{\text{2}}{\text{. 89}}}}}\right.

\!\!\!\!\overline{\,\,\,\vphantom 1{{{\text{2}}{\text{. 89}}}}}}

\limits^{\displaystyle \,\,\, 1} \\

  \dfrac{{ - 1}}{{{\text{ 1}}}} \\

\end{gathered} \]

We have a decimal after 2, so we place a decimal in the quotient.

Now, we bring the next pair down and the number becomes 189, we now need to find a number such that 2x multiplied with x gives 189.

We know that 27 multiplied with 7 gives 189.

\[\begin{gathered}

  {\text{ }}1\mathop{\left){\vphantom{1\begin{gathered}

  {\text{ 2}}{\text{. 89}} \\

   - {\text{1 }} \downarrow \\

\end{gathered} }}\right.

\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}

  {\text{ 2}}{\text{. 89}} \\

   - {\text{1 }} \downarrow \\

\end{gathered} }}}

\limits^{\displaystyle \,\,\, {1.7}} \\

  27\left){\vphantom{1\begin{gathered}

  {\text{ }}1{\text{ 89}} \\

   - \dfrac{{1{\text{ }}89{\text{ }}}}{{\dfrac{{{\text{ }}0{\text{ }}}}{{}}}} \\

\end{gathered} }}\right.

\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}

  {\text{ }}1{\text{ 89}} \\

   - \dfrac{{1{\text{ }}89{\text{ }}}}{{\dfrac{{{\text{ }}0{\text{ }}}}{{}}}} \\

\end{gathered} }} \\

\end{gathered} \]

Hence, the square root of 2.89 is 1.7.


Note: Be careful when placing the decimal in the answer. You can also check if your answer is correct or not by squaring your answer.