Which sign makes the statement true?

Question

1.8 ? 3(the square root sign)10
< or >

Answer 1

To determine which sign makes the statement true, we need to compare \(1.8\) with \(3\sqrt{10}\).

First, let's calculate \(3\sqrt{10}\):

1. Find \(\sqrt{10}\): \(\sqrt{10} \approx 3.162\) (since \(3.162^2 \approx 10\))

2. Now multiply by \(3\): \[ 3\sqrt{10} \approx 3 \times 3.162 \approx 9.486 \]

Now we can compare \(1.8\) with \(9.486\):

Since \(1.8 < 9.486\), we find that:

\[ 1.8 < 3\sqrt{10} \]

Therefore, the correct sign is \(<\).

So the final answer is: \[ 1.8 < 3\sqrt{10} \]