Using a number line, what whole number and rational number to the nearest half is √70 between?

Question

GPT-4o mini · Answer

To find the whole number and the rational number to the nearest half that $ \sqrt{70} $ is between, we first need to estimate $ \sqrt{70} $.

We know that:

$ 8^2 = 64 $
$ 9^2 = 81 $

Since $ 64 < 70 < 81 $, it follows that:

\[ 8 < \sqrt{70} < 9 \]

Next, we can get a better estimate of $ \sqrt{70} $ by calculating it:

\[ \sqrt{70} \approx 8.37 \]

Now let's find the nearest half. The nearest halves around $ 8.37 $ are $ 8.5 $ and $ 8.0 $. Since $ 8.37 $ is closer to $ 8.5 $, we can round $ \sqrt{70} $ to:

\[ 8.37 \approx 8.5 \]

Therefore, $ \sqrt{70} $ is between the whole number $ 8 $ and the rational number $ 8.5 $.

In conclusion, $ \sqrt{70} $ is:

Between the whole number: 8
And the rational number to the nearest half: 8.5

joe mawna · Answer

put this in normal ppl words

GPT-4o mini · Answer

To find out where $ \sqrt{70} $ falls on a number line, we start by figuring out its approximate value. We know that: - $ 8^2 = 64 $ - $ 9^2 = 81 $ Since $ 70 $ is between $ 64 $ and $ 81 $, we can say: $$ 8 < \sqrt{70} < 9 $$ Now, if we calculate $ \sqrt{70} $, we get about $ 8.37 $. Next, we want to see which whole number and which value to the nearest half $ \sqrt{70} $ is closest to. The nearest half numbers around $ 8.37 $ are $ 8.0 $ and $ 8.5 $. Since $ 8.37 $ is closer to $ 8.5 $, we choose that. So, in simple terms: - $ \sqrt{70} $ is between the whole number: **8** - And the nearest half: **8.5**