To compare \( \sqrt{81} \) and \( \sqrt{88} \), we can start by calculating the square roots of 81 and 88.
- \( \sqrt{81} = 9 \)
- \( \sqrt{88} \) can be approximated. We know that \( \sqrt{88} \) is slightly less than \( \sqrt{100} = 10 \), and we can find a closer approximation.
To find \( \sqrt{88} \):
- We know \( \sqrt{88} \) is between \( 9 \) and \( 10 \).
- Let's calculate \( 9.3^2 \) and \( 9.4^2 \) to narrow it down:
- \( 9.3^2 = 86.49 \)
- \( 9.4^2 = 88.36 \)
Since \( 86.49 < 88 < 88.36 \), we can conclude that \( 9.3 < \sqrt{88} < 9.4 \).
So now we can compare:
- We know \( \sqrt{81} = 9 \)
- and \( \sqrt{88} \) is approximately between \( 9.3 \) and \( 9.4 \).
Thus, we can write the inequality: \[ \sqrt{81} < \sqrt{88} \] or \[ 9 < \sqrt{88} \]
This shows that \( \sqrt{81} \) is less than \( \sqrt{88} \).
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