To subtract these radicals together their radicands must be the same:

8\( \sqrt{20} \) - 7\( \sqrt{5} \)
8\( \sqrt{4 \times 5} \) - 7\( \sqrt{5} \)
8\( \sqrt{2^2 \times 5} \) - 7\( \sqrt{5} \)
(8)(2)\( \sqrt{5} \) - 7\( \sqrt{5} \)
16\( \sqrt{5} \) - 7\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

2,389,000 in scientific notation is 2.389 x 10⁶

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 5}{3 x 5} \) - \( \frac{6 x 3}{5 x 3} \)

\( \frac{35}{15} \) - \( \frac{18}{15} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{35 - 18}{15} \) = \( \frac{17}{15} \) = 1\(\frac{2}{15}\)

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{44} \) = \( \frac{\frac{28}{4}}{\frac{44}{4}} \) = \( \frac{7}{11} \)

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.