Question

1. which statement is true?

a. $7 < \sqrt{65} < 8$
b. $4 < \sqrt{13} < 5$
c. $6 < \sqrt{33} < 7$
d. $9 < \sqrt{91} < 10$

Explanation:

Step1: Square all bounds for Option A

$7^2=49$, $8^2=64$, $\sqrt{65}^2=65$

Step2: Check if 65 is between 49 and 64

$65>64$, so $7<\sqrt{65}<8$ is false.

Step3: Square all bounds for Option B

$4^2=16$, $5^2=25$, $\sqrt{13}^2=13$

Step4: Check if 13 is between 16 and 25

$13<16$, so $4<\sqrt{13}<5$ is false.

Step5: Square all bounds for Option C

$6^2=36$, $7^2=49$, $\sqrt{33}^2=33$

Step6: Check if 33 is between 36 and 49

$33<36$, so $6<\sqrt{33}<7$ is false.

Step7: Square all bounds for Option D

$9^2=81$, $10^2=100$, $\sqrt{91}^2=91$

Step8: Check if 91 is between 81 and 100

$81<91<100$, so $9<\sqrt{91}<10$ is true.

Answer:

D. $9 < \sqrt{91} < 10$