Question
The value of \( \sqrt{215} \) is between two consecutive integers. What are these two integers?
Ask by Zimmerman Simmons. in Spain
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The value of \( \sqrt{215} \) is between 14 and 15.
Solution
To determine between which two consecutive integers the value of \( \sqrt{215} \) lies, we can look at the squares of consecutive integers:
- \( 14^2 = 196 \)
- \( 15^2 = 225 \)
Since \( 215 \) is between \( 196 \) and \( 225 \), it follows that:
\[ 14 < \sqrt{215} < 15 \]
**Answer:** \( 14 \) and \( 15 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the two consecutive integers between which \( \sqrt{215} \) lies, we can start by identifying the perfect squares closest to 215. The perfect square \( 14^2 = 196 \) is less than 215, and \( 15^2 = 225 \) is greater than 215. Since \( 196 < 215 < 225 \), it follows that \( 14 < \sqrt{215} < 15 \). Therefore, the two consecutive integers are 14 and 15.
