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

7\( \sqrt{12} \) + 3\( \sqrt{3} \)
7\( \sqrt{4 \times 3} \) + 3\( \sqrt{3} \)
7\( \sqrt{2^2 \times 3} \) + 3\( \sqrt{3} \)
(7)(2)\( \sqrt{3} \) + 3\( \sqrt{3} \)
14\( \sqrt{3} \) + 3\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

The factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 the greatest factor 60 and 52 have in common.

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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%

By buying two shirts, Damon will save $36 x \( \frac{50}{100} \) = \( \frac{$36 x 50}{100} \) = \( \frac{$1800}{100} \) = $18.00 on the second shirt.

So, his total cost will be
$36.00 + ($36.00 - $18.00)
$36.00 + $18.00
$54.00

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)