The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

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 35% the radius (and, consequently, the total area) increases by \( \frac{35\text{%}}{2} \) = 17\(\frac{1}{2}\)%

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

6\( \sqrt{32} \) - 2\( \sqrt{2} \)
6\( \sqrt{16 \times 2} \) - 2\( \sqrt{2} \)
6\( \sqrt{4^2 \times 2} \) - 2\( \sqrt{2} \)
(6)(4)\( \sqrt{2} \) - 2\( \sqrt{2} \)
24\( \sqrt{2} \) - 2\( \sqrt{2} \)

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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-1z⁵ + 7z⁵
(-1 + 7)z⁵
6z⁵

To multiply terms with radicals, multiply the coefficients and radicands separately:

4\( \sqrt{3} \) x 6\( \sqrt{6} \)
(4 x 6)\( \sqrt{3 \times 6} \)
24\( \sqrt{18} \)

Now we need to simplify the radical:

24\( \sqrt{18} \)
24\( \sqrt{2 \times 9} \)
24\( \sqrt{2 \times 3^2} \)
(24)(3)\( \sqrt{2} \)
72\( \sqrt{2} \)