Question

what integer is between 2π + 1 and √72 ?

Explanation:

Step1: Calculate \(2\pi + 1\)

We know that \(\pi\approx3.14\), so \(2\pi\approx2\times3.14 = 6.28\). Then \(2\pi + 1\approx6.28+1 = 7.28\).

Step2: Calculate \(\sqrt{72}\)

We know that \(\sqrt{64}=8\) and \(\sqrt{81}=9\), and \(64\lt72\lt81\), so \(\sqrt{72}\) is between \(8\) and \(9\). More precisely, \(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\approx6\times1.414 = 8.484\).

Step3: Find the integer between them

We have \(2\pi + 1\approx7.28\) and \(\sqrt{72}\approx8.484\). The integer between \(7.28\) and \(8.484\) is \(8\).

Answer:

\(8\)