Question

What is the square root of 112?

Answer 1

Hint: Here we have to find the square root of 112. The square root of 112 is actually the number which is not a perfect square. The symbol of the square root is denoted by \[\left( \sqrt{{}} \right)\]. Any number inside this symbol (square root) will give the original number when multiplied by itself. We can now use the long division method to find the answer.

Complete step-by-step answer:
Given that- Find the value of square root 112 in its simplest form.
We can now find the answer using the long division method by the following steps.
Step 1: We can draw lines over pairs of digits from right to left
Step 2: let us find the greatest number whose square is less than or equal to the digits in the first group
Step 3: We can take this number as the divisor and the quotient of the first group and find the reminder
Step 4: Now we can move the digits from the second group besides the reminder to get the new dividend.
Step 5: We can double the first divisor and bring it down as the new divisor.
Step 6: let us complete the divisor and continue the division.
Step 7: Now we can put the decimal part in the square root as soon as the integral part is exhausted
Step 8: we can repeat the process till the remainder becomes zero\[\]
\[\begin{align}
  & \dfrac{1}{\dfrac{\begin{align}
  & 20 \\
 & \\
\end{align}}{\dfrac{205}{\dfrac{{}}{2108}}}}\overset{\text{1 0 }\text{. 5 8 3 }}{\overline{\left){\underline{\dfrac{\begin{align}
  & \text{1 12 }.\text{ }00\text{ }00\text{ }00 \\
 & \text{1 }\downarrow \text{ }\downarrow \text{ } \\
\end{align}}{\dfrac{\begin{align}
  & 12 \\
 & 0 \\
\end{align}}{\dfrac{\begin{align}
  & \text{ 12 }00 \\
 & \text{ 10 25} \\
\end{align}}{\begin{align}
  & \text{ 1 7 5 00} \\
 & \text{ 1 6 8 64} \\
\end{align}}}}}}\right.}} \\
 & \text{ 636} \\
\end{align}\]
Therefore, the square root of 112 is 10.583.

Note: The square root of any positive integer can be found by various methods such as, Average method, Number line method and Long division method. Here in this given problem ‘112’ is not a perfect square so we have to use any of the three methods to find its root.