Question
Between which two consecutive integers does \( \sqrt{150} \) lie?
Ask by Reed Wells. in South Africa
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{150} \) lies between 12 and 13.
Solution
To find between which two consecutive integers \( \sqrt{150} \) lies, we can start by identifying the perfect squares that are closest to 150.
1. Calculate the perfect squares around 150:
- \( 12^2 = 144 \)
- \( 13^2 = 169 \)
2. Since \( 144 < 150 < 169 \), we can conclude that:
\[
12 < \sqrt{150} < 13
\]
Thus, \( \sqrt{150} \) lies between the consecutive integers 12 and 13.
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Simplify this solution Bonus Knowledge
To find between which two consecutive integers \( \sqrt{150} \) lies, we can estimate the square root by identifying perfect squares around 150. Since \( 12^2 = 144 \) and \( 13^2 = 169 \), we see that \( 144 < 150 < 169 \). Thus, \( 12 < \sqrt{150} < 13 \). Therefore, \( \sqrt{150} \) lies between the consecutive integers 12 and 13.
