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Let \( s \) be any real number such that \( 4 < \sqrt{s} < 9 \). Which of the following is a possible value of \( s \)?

A. 2.5
B. 7.6
C. 12.7
D. 39.3
E. 82.4

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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