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

3\( \sqrt{175} \) + 5\( \sqrt{7} \)
3\( \sqrt{25 \times 7} \) + 5\( \sqrt{7} \)
3\( \sqrt{5^2 \times 7} \) + 5\( \sqrt{7} \)
(3)(5)\( \sqrt{7} \) + 5\( \sqrt{7} \)
15\( \sqrt{7} \) + 5\( \sqrt{7} \)

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

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:

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

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{7 x 4}{2 x 4} \) - \( \frac{3 x 1}{8 x 1} \)

\( \frac{28}{8} \) - \( \frac{3}{8} \)

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

\( \frac{28 - 3}{8} \) = \( \frac{25}{8} \) = 3\(\frac{1}{8}\)

By buying two shirts, Frank will save $35 x \( \frac{35}{100} \) = \( \frac{$35 x 35}{100} \) = \( \frac{$1225}{100} \) = $12.25 on the second shirt.