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

5\( \sqrt{63} \) - 2\( \sqrt{7} \)
5\( \sqrt{9 \times 7} \) - 2\( \sqrt{7} \)
5\( \sqrt{3^2 \times 7} \) - 2\( \sqrt{7} \)
(5)(3)\( \sqrt{7} \) - 2\( \sqrt{7} \)
15\( \sqrt{7} \) - 2\( \sqrt{7} \)

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

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 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%

To simplify a radical, factor out the perfect squares:

\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)

First, solve for \( \left|x + 8\right| \):

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

The value inside the absolute value brackets can be either positive or negative so (x + 8) must equal + 8 or -8 for \( \left|x + 8\right| \) to equal 8:

So, x = -16 or x = 0.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).