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Which value of [tex]\( a \)[/tex] would make the inequality statement true?

[tex]\[ 9.53 \ \textless \ \sqrt{a} \ \textless \ 9.54 \][/tex]

A. 85
B. 88
C. 91
D. 94



Answer :

GinnyAnswer
To determine the value of [tex]\( a \)[/tex] that makes the inequality [tex]\( 9.53 < \sqrt{a} < 9.54 \)[/tex] true, we need to find the range of [tex]\( a \)[/tex] that satisfies this inequality.

1. First, square the lower bound of the inequality [tex]\( 9.53 \)[/tex]:

[tex]\[ 9.53^2 = 90.7609 \][/tex]

2. Next, square the upper bound of the inequality [tex]\( 9.54 \)[/tex]:

[tex]\[ 9.54^2 = 91.0116 \][/tex]

So, the inequality [tex]\( 9.53 < \sqrt{a} < 9.54 \)[/tex] translates to:

[tex]\[ 90.7609 < a < 91.0116 \][/tex]

3. Now we need to identify which of the given choices falls within the range [tex]\( (90.7609, 91.0116) \)[/tex]. The choices provided are:

- 85
- 88
- 91
- 94

4. Let's analyze each option to see if it falls within our calculated range:

- 85 is not within the range [tex]\( (90.7609, 91.0116) \)[/tex]
- 88 is not within the range [tex]\( (90.7609, 91.0116) \)[/tex]
- 91 is within the range [tex]\( (90.7609, 91.0116) \)[/tex]
- 94 is not within the range [tex]\( (90.7609, 91.0116) \)[/tex]

Thus, the value of [tex]\( a \)[/tex] that makes the inequality [tex]\( 9.53 < \sqrt{a} < 9.54 \)[/tex] true is:

[tex]\[ \boxed{91} \][/tex]

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