To determine between which two values [tex]\(\sqrt{56}\)[/tex] lies, we first need to consider the approximate location of [tex]\(\sqrt{56}\)[/tex] on the number line.
We are given several options to consider:
(a) between 7.0 and 7.1
(b) between 7.2 and 7.3
(c) between 7.4 and 7.5
(d) between 7.6 and 7.7
Let's evaluate [tex]\(\sqrt{56}\)[/tex].
We know that [tex]\(7^2 = 49\)[/tex] and [tex]\(8^2 = 64\)[/tex]. Since [tex]\(56\)[/tex] is between [tex]\(49\)[/tex] and [tex]\(64\)[/tex], it follows that [tex]\(\sqrt{56}\)[/tex] is between [tex]\(7\)[/tex] and [tex]\(8\)[/tex].
We need to narrow it down further to determine between which of the given intervals [tex]\(\sqrt{56}\)[/tex] falls. Looking at the options, we notice that the correct interval is between 7.4 and 7.5.
Therefore, the correct answer is:
(c) 7.4 and 7.5
