Question

between which two whole numbers do both the irrational numbers $sqrt{54}$ and $sqrt{60}$ lie?
a 54 and 60
b 49 and 64
c 27 and 30
d 7 and 8

Explanation:

Step1: Recall square - number relationships

We know that \(7^2=49\) and \(8^2 = 64\).

Step2: Compare square - roots

Since \(49<54<60<64\), then \(\sqrt{49}<\sqrt{54}<\sqrt{60}<\sqrt{64}\).

Step3: Simplify square - roots

\(\sqrt{49} = 7\) and \(\sqrt{64}=8\), so \(7<\sqrt{54}<\sqrt{60}<8\).

Answer:

D. 7 and 8