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The square root of \[248\] should lie between ______
\[\begin{align}
  & \text{A}\text{.13 and 14} \\
 & \text{B}\text{.14 and 15} \\
 & \text{C}\text{.15 and 16} \\
 & \text{D}\text{.none of these} \\
\end{align}\]

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Last updated date: 19th Jul 2024
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Answer
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Hint: In order to find the range of the square root of \[248\], we can consider each of the options and find the squares of the upper limit and the lower limit of the given range. After finding the squares, we can decide from the obtained squares range where the square root of \[248\] lies.

Complete step by step answer:
Now let us briefly consider the squares and square roots. Square of a number is obtained when a number is being multiplied itself twice. The number being multiplied is called as the square root of the obtained square. A square root of a larger number can be found by the prime factorisation method, long division method, average method, guess and check method, number line method and repeated subtraction method.
Now let us find the range of the square root of \[248\] lies.
Now let us consider the first option i.e. \[\text{13 and 14}\]
Now we will be finding the square of the upper limit and the lower limit.
The square of \[\text{13 }\]is \[\text{169}\].
The square of \[\text{14}\] is \[\text{196}\].
\[\therefore \] We can clearly understand that the square root of \[248\] does not lie between \[\text{13 and 14}\]
Now we will be considering the second option i.e. \[\text{14 and 15}\]
Let us find the squares the of \[\text{14 and 15}\]
The square of \[\text{14}\] is \[\text{196}\].
The square of \[\text{15}\] is \[\text{225}\].
\[\therefore \] We can clearly understand that the square root of \[248\] does not lie between \[\text{14 and 15}\].
Now we will be considering the third option i.e. \[\text{15 and 16}\].
Let us find the squares of \[\text{15 and 16}\].
The square of \[\text{15}\] is \[\text{225}\].
The square of \[\text{16}\] is \[\text{256}\].
\[\therefore \] We can clearly understand that the square root of \[248\] lies between \[\text{15 and 16}\].

So, the correct answer is “Option C”.

Note: We must always have a note that the square and the square root of a number are the inverse operations performed on the same number. We can also say that the square root of the square of a number is the number itself and vice versa.