Question

Write the correct answer from the given four options.
Which letter best represents the location of \[\sqrt {25} \] on a number line?

A) A
B) B
C) C
D) D

Answer 1

Hint:
Here, we will find the square root of the given number 25. using the prime factorization method. The root of the 25 will be a number that should be represented on the number line. By looking carefully on the given number line we will be able to find which letter represents the number to get the required answer.

Complete step by step solution:
We are required to locate \[\sqrt {25} \] on a number line.
First, we will find the square root of 25.
In order to find the square root of 25, we will do the prime factorization of 25.
Now, factorization is a method of writing an original number as the product of its various factors.
Also, prime numbers are those numbers which are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself.
Hence, prime factorization is a method in which we write the original number as the product of various prime numbers.
Therefore, 25 can be written as:
\[25 = 5 \times 5\]
Now, since, we are required to find the square root,
We will take only one prime number out of a pair of the same prime numbers.
\[ \Rightarrow \sqrt {25} = 5\]
Hence, the square root of 25 is 5.
Therefore, we are required to locate 5 on the number line.
From the given number line, point C represents the number 5.

Thus, option C is the correct answer.

Note:
An alternate way to find the square root of the given number is by using Division method.
\[\begin{array}{*{20}{r}}{}&5\\5&{\left| \!{\overline {\,
 \begin{array}{l}\overline {25} \\\underline { - 25} \\0\end{array} \,}} \right. }\end{array}\]

In this method, we start pairing the numbers by taking a bar starting from the unit’s place. We take the largest possible number whose square will be less than or equal to the leftmost pair.
But since, in this question, we were required to find the square root of a two digit number, hence, only one bar was required and that number was a perfect square, thus, in just one step we were able to find its required square root.
Thus, the square root of 25 is 5.
And, from the number line, point C represents the location of the number 5.
Thus, option C is the correct answer.
Hence, we can use either of the two ways to answer this question.