Using a number line, what whole number and rational number to the nearest half is √30

Question

between?

Show your work.

(1 point)
√30 is between___ and____

Answer 1

To find the two numbers between which \(\sqrt{30}\) lies, let's start by calculating its approximate value.

1. Estimate \(\sqrt{30}\):

   We know that \(\sqrt{25} = 5\) and \(\sqrt{36} = 6\). Thus, we can establish that: \[ 5 < \sqrt{30} < 6 \]

2. Calculating \(\sqrt{30}\) more precisely:

   We can use a calculator to find the value of \(\sqrt{30}\): \[ \sqrt{30} \approx 5.477 \]

3. Determine the nearest half:

   The nearest half to \(5.477\) is \(5.5\). Therefore, we can express \(\sqrt{30}\) as being between: \[ 5 \text{ and } 5.5 \]

4. Final notation:

   The whole number it is between is \(5\) and the rational number to the nearest half is \(5.5\).

So, we have: \[ \sqrt{30} \text{ is between } 5 \text{ and } 5.5. \]