To find the two numbers between which \(\sqrt{30}\) lies, let's start by calculating its approximate value.
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Estimate \(\sqrt{30}\):
We know that \(\sqrt{25} = 5\) and \(\sqrt{36} = 6\). Thus, we can establish that: \[ 5 < \sqrt{30} < 6 \]
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Calculating \(\sqrt{30}\) more precisely:
We can use a calculator to find the value of \(\sqrt{30}\): \[ \sqrt{30} \approx 5.477 \]
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Determine the nearest half:
The nearest half to \(5.477\) is \(5.5\). Therefore, we can express \(\sqrt{30}\) as being between: \[ 5 \text{ and } 5.5 \]
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Final notation:
The whole number it is between is \(5\) and the rational number to the nearest half is \(5.5\).
So, we have: \[ \sqrt{30} \text{ is between } 5 \text{ and } 5.5. \]