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

7\( \sqrt{32} \) - 5\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) - 5\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) - 5\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) - 5\( \sqrt{2} \)
28\( \sqrt{2} \) - 5\( \sqrt{2} \)

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

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 5 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 5 x 4 = 20 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 20 - 8 = 12 new staff for the busy season.

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:

\( \sqrt{\frac{49}{36}} \)
\( \frac{\sqrt{49}}{\sqrt{36}} \)
\( \frac{\sqrt{7^2}}{\sqrt{6^2}} \)
\( \frac{7}{6} \)
1\(\frac{1}{6}\)

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{9} \) ÷ \( \frac{2}{8} \) = \( \frac{3}{9} \) x \( \frac{8}{2} \)

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

\( \frac{3}{9} \) x \( \frac{8}{2} \) = \( \frac{3 x 8}{9 x 2} \) = \( \frac{24}{18} \) = 1\(\frac{1}{3}\)