The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 3 factors [1, 2, 4] making 4 the greatest factor 76 and 24 have in common.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{72} \) = \( \frac{\frac{40}{8}}{\frac{72}{8}} \) = \( \frac{5}{9} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{64}} \)
\( \frac{\sqrt{81}}{\sqrt{64}} \)
\( \frac{\sqrt{9^2}}{\sqrt{8^2}} \)
\( \frac{9}{8} \)
1\(\frac{1}{8}\)

First, solve for \( \left|c + 5\right| \):

\( \left|c + 5\right| \) - 8 = 3
\( \left|c + 5\right| \) = 3 + 8
\( \left|c + 5\right| \) = 11

The value inside the absolute value brackets can be either positive or negative so (c + 5) must equal + 11 or -11 for \( \left|c + 5\right| \) to equal 11:

So, c = -16 or c = 6.