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

4\( \sqrt{175} \) - 3\( \sqrt{7} \)
4\( \sqrt{25 \times 7} \) - 3\( \sqrt{7} \)
4\( \sqrt{5^2 \times 7} \) - 3\( \sqrt{7} \)
(4)(5)\( \sqrt{7} \) - 3\( \sqrt{7} \)
20\( \sqrt{7} \) - 3\( \sqrt{7} \)

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

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 18 - 9 = 9 new staff for the busy season.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (5 + 4) ÷ 3 x 2 - 5²
P: 5 + (9) ÷ 3 x 2 - 5²
E: 5 + 9 ÷ 3 x 2 - 25
MD: 5 + \( \frac{9}{3} \) x 2 - 25
MD: 5 + \( \frac{18}{3} \) - 25
AS: \( \frac{15}{3} \) + \( \frac{18}{3} \) - 25
AS: \( \frac{33}{3} \) - 25
AS: \( \frac{33 - 75}{3} \)
\( \frac{-42}{3} \)
-14

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{5} \) x \( \frac{2}{5} \) = \( \frac{2 x 2}{5 x 5} \) = \( \frac{4}{25} \) = \(\frac{4}{25}\)