Question
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Insert the two whole numbers on both sides of \( v \) \( \square<\sqrt{24}<\square \)

Ask by Hardy Vega. in South Africa
Mar 09,2025

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Answer

The two whole numbers are 4 and 5.

Solution

We need to find two whole numbers such that \[ \square < \sqrt{24} < \square. \] **Step 1.** Find two consecutive whole numbers \(a\) and \(a+1\) such that \[ a^2 < 24 < (a+1)^2. \] **Step 2.** Test \(a = 4\): \[ 4^2 = 16 \quad \text{and} \quad 5^2 = 25. \] Since \[ 16 < 24 < 25, \] it follows that \[ 4 < \sqrt{24} < 5. \] Thus, the two whole numbers are \(4\) and \(5\).

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The square root of 24 can be approximated to about 4.9, as it's between the squares of 4 and 5 (since \(4^2=16\) and \(5^2=25\)). Therefore, the two whole numbers that fit the inequality are 4 and 5. So we can write it as: \( 4 < \sqrt{24} < 5 \)

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