Question

The number of integers between \[- \sqrt 8 \] and \[\sqrt {32} \] is
A 5
B 6
C 7
D 8

Answer 1

Hint:In this problem, first we need to find the approximate values of \[- \sqrt 8 \] and \[\sqrt {32}\]. Now, plot the obtained values over the number line. Next, count the number of integers between \[- \sqrt 8\] and \[\sqrt {32}\].

Complete step-by-step answer:
The approximate value of \[- \sqrt 8\] is calculated as follows:
\[\begin{gathered}
  \,\,\,\,\, - \sqrt 8 \\
   \Rightarrow - 2\sqrt 2 \\
   \Rightarrow - 2\left( {1.414} \right) \\
   \Rightarrow - 2.828 \\
\end{gathered}\]
The approximate value of \[\sqrt {32} \] is calculated as follows:
\[\begin{gathered}
  \,\,\,\,\,\sqrt {32} \\
   \Rightarrow \sqrt {{2^5}} \\
   \Rightarrow \sqrt 2 \cdot \sqrt {{2^4}} \\
   \Rightarrow {2^2}\sqrt 2 \\
   \Rightarrow 4\left( {1.414} \right) \\
   \Rightarrow 5.656 \\
\end{gathered}\]
Now, \[- \sqrt 8\] and \[\sqrt {32} \] can be drawn over the number line as shown below.

It can be counted over the number line that there are 8 integers lying between\[- \sqrt 8\] and \[\sqrt {32} \].
Thus, the option (D) is the correct answer.

Note: Integers are defined as positive or negative whole numbers which cannot be a fraction. In this problem, there are 8 integers starting from -2 to 5 lying between \[- \sqrt 8\] and \[\sqrt {32} \].