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:

\( \sqrt{\frac{36}{81}} \)
\( \frac{\sqrt{36}}{\sqrt{81}} \)
\( \frac{\sqrt{6^2}}{\sqrt{9^2}} \)
\(\frac{2}{3}\)

The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.

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

6\( \sqrt{2} \) x 4\( \sqrt{8} \)
(6 x 4)\( \sqrt{2 \times 8} \)
24\( \sqrt{16} \)

Now we need to simplify the radical:

24\( \sqrt{16} \)
24\( \sqrt{4^2} \)
(24)(4)
96

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.

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 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%