Which number line correctly compares √24 and 4.256?

To determine which number line correctly compares √24 and 4.256, let’s first calculate √24.

√24 can be simplified as:

√24 = √(4 * 6) = √4 * √6 = 2√6.

Now, we estimate √6. Since 2.4² is 5.76 and 2.5² is 6.25, we know that √6 is approximately between 2.4 and 2.5.

Calculating further, we can find that:
2.45² = 6.0025, which indicates that √6 is slightly less than 2.45.

Thus,

√24 = 2√6 is approximately 2 * 2.45 = 4.9.

So, we know that:

√24 ≈ 4.9 and 4.256 < 4.9.

This means that √24 is greater than 4.256.

Now look at the number lines provided (A, B, C, D) and find the one where √24 is placed to the right of 4.256. This will indicate that √24 is indeed greater.

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