The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

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

9\( \sqrt{18} \) - 6\( \sqrt{2} \)
9\( \sqrt{9 \times 2} \) - 6\( \sqrt{2} \)
9\( \sqrt{3^2 \times 2} \) - 6\( \sqrt{2} \)
(9)(3)\( \sqrt{2} \) - 6\( \sqrt{2} \)
27\( \sqrt{2} \) - 6\( \sqrt{2} \)

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

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

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

\( \frac{9 x 3}{4 x 3} \) + \( \frac{8 x 2}{6 x 2} \)

\( \frac{27}{12} \) + \( \frac{16}{12} \)

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

\( \frac{27 + 16}{12} \) = \( \frac{43}{12} \) = 3\(\frac{7}{12}\)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $200
i = 0.01 x $200
i = $2

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%