Question

approximating values of irrational numbers - item 92912. use the drop - down menus to complete each statement to show why √21 is between 4 and 5. 16 < 21 < 25, so √21 is between and. this means that √21 is between.

Explanation:

Step1: Recall square - root property

If \(a^2 < b < c^2\), then \(\sqrt{a^2}<\sqrt{b}<\sqrt{c^2}\), where \(a,b,c>0\).
Since \(16 < 21 < 25\), and \(16 = 4^2\), \(25=5^2\), we have \(\sqrt{16}<\sqrt{21}<\sqrt{25}\).

Step2: Simplify square - roots

We know that \(\sqrt{16}=4\) and \(\sqrt{25} = 5\). So \(\sqrt{21}\) is between \(4\) and \(5\).

Answer:

The first two blanks: 4, 5. The third blank: 4 and 5.