Question

Find the square root of 79.21 using the long division method.

Answer 1

Hint: Here, we have to find the square root of 79.21. Square root of a number means the number which when multiplied by itself gives the original number. The square root of a number is denoted by the radical sign $\sqrt {} $ and the value inside this is known as radicand. Here, we are going to use the long division method to find the square root of 79.21.

Complete step-by-step answer:
In this question, we are given a number and we have to find its square root using a long division method.
Given number: $79.21$
Now, we can find the square root of a number in many ways but in this question, we are asked to use the long division method so we will use the long division method only.
A square root of a number means the number when multiplied by itself gives the original number. Let us see the steps to find the square root using the long division method.
Steps to find square root using Square root:
Step 1:
Write down the number whose square root is to be found and place a bar over the pairs of two numbers from units place.
\[\overline{79}\overline{.21}\]
Step 2:
For the divisor, take the largest number whose square is less than or equal to the first pair of numbers. Here, the first pair is 79. So, 8 is the largest number whose square is less than 79. So, we will divide by 8.
\[\begin{align}
  &\;\;\;\;\;\;\; 8 \\
 & 8\left| \!{\overline {\,
 \begin{align}
  & \overline{79}.\overline{21} \\
 & \underline{64} \\
 & 15 \\
\end{align} \,}} \right. \\
\end{align}\]
Step 3:
Bring down the next pair. Here our next pair is 21.
\[\begin{align}
  &\;\;\;\;\;\;\; 8 \\
 & 8\left| \!{\overline {\,
 \begin{align}
  & \overline{79}.\overline{21} \\
 & \underline{64} \\
 & 1521 \\
\end{align} \,}} \right. \\
\end{align}\]
Step 4:
Now, double the value of the quotient and write it in divisor. For the second digit, we need to write such a number which when multiplied by the new number obtained gives us less than or equal to the dividend.
Here the quotient is 8. So, one digit of the divisor will be 16. Now, if we take the third digit 9 and then multiply 169 by 9, we get the product equal to our dividend.
$\Rightarrow 169\times 9=1521$
\[\begin{align}
  &\;\;\;\;\;\;\; 8.9 \\
 & 8\left| \!{\overline {\,
 \begin{align}
  & \overline{79}.\overline{21} \\
 & \underline{64} \\
 & 1521 \\
\end{align} \,}} \right. \\
 & 169\left| \!{\overline {\,
 \begin{align}
  & 1521 \\
 & \underline{1521} \\
 & 0 \\
\end{align} \,}} \right. \\
\end{align}\]
Hence, the square root of $79.21$ is $8.9$.

Note: If this method seems complicated to you, you can also use the log method to find the square root of $79.21$. For that, let the square root of $79.21$ be $x$.
$\begin{align}
  & \Rightarrow x=\sqrt{79.21} \\
 & \Rightarrow x={{\left( 79.21 \right)}^{\dfrac{1}{2}}} \\
 & \Rightarrow \log x=\log {{\left( 79.21 \right)}^{\dfrac{1}{2}}} \\
 & \Rightarrow \log x=\dfrac{1}{2}\log \left( 79.21 \right) \\
 & \Rightarrow \log x=\dfrac{1}{2}\left( 1.898780013 \right) \\
 & \Rightarrow \log x=0.9493900065 \\
 & \Rightarrow x=anti\log \left( 0.9493900065 \right) \\
 & \Rightarrow x=8.89 \\
\end{align}$