Answer :
The possible real number for the variable s is 39.3 (letter D).
Power and Square Roots
It is common in math solutions, you multiply a number by itself. See the examples below.
2 x 2 =4
3 x 3 = 9
4 x 4 = 16
In math, you can use the power to represent a multiply a number by itself using the operation power. Let's consider the previous example for a better understanding.
2 x 2 = 2²
3 x 3 = 3²
4 x 4 = 4²
Therefore, the power represents the number of times the numeral repeats in a product. It is important to know that the inverse operation of power is the root. Thus,
2²=4 and [tex]\sqrt{4}[/tex]= 2
The question asks you the possible value of s.
If [tex]4 < \sqrt{s}[/tex], you can apply power operation on both sides, for eliminating the root.
[tex](4)^2 < (\sqrt{s})^2\\ \\ 16 < s[/tex]
Another inequality is [tex]\sqrt{s} < 9[/tex]. Then, one more time you will apply power operation on both sides, for eliminating the root.
[tex](\sqrt{s})^2 < (9)^2 \\ \\ s < 81[/tex]
Combining the intervals you have: 16< s< 81. Now, let's analyze the given options.
A. 2.5 - It is not contained in the given range 16< s< 81.
B. 7.6 - It is not contained in the given range 16< s< 81.
C. 12.7 - It is not contained in the given range 16< s< 81.
D. 39.3 - It is contained in the given range 16< s< 81.
E. 82.4 - It is not contained in the given range 16< s< 81.
Read more about the square roots here:
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