Question

How do you simplify the square root of \[244\]?

Answer 1

Hint: In the given question, we have been asked to find the simplified form of the square root of an even natural number. To solve this question, we just need to know how to solve the square root. If the number is a perfect square, then it will have no integer left in the square root. But if it is not a perfect square, then it has at least one integer in the square root.

Complete step-by-step answer:
The given number whose simplified form is to be found is the square root of \[244\], or we have to evaluate the value of \[\sqrt {244} \].
First, we find the prime factorization of \[244\] and club the pair(s) of equal integers together.
\[\begin{array}{l}{\rm{ }}2\left| \!{\underline {\,
  {244} \,}} \right. \\{\rm{ }}2\left| \!{\underline {\,
  {122} \,}} \right. \\61\left| \!{\underline {\,
  {61} \,}} \right. \\{\rm{ }}\left| \!{\underline {\,
  1 \,}} \right. \end{array}\]
Hence, \[244 = 2 \times 2 \times 61 = {2^2} \times 61\]
Hence, \[\sqrt {244} = \sqrt {{{\left( 2 \right)}^2} \times 61} = 2\sqrt {61} \]
Thus, the simplified form of \[\sqrt {244} \] is \[2\sqrt {61} \].

Note: In the given question, we had to calculate the square root of a number which is not a perfect square. We did by following the above method. The point where there is a big chance of making mistakes is when we divide the numbers. The smallest error of writing the quotient with even just one-digit wrong gives the wrong answer. So, it is important to keep checking the calculations.