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

8\( \sqrt{175} \) - 2\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) - 2\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) - 2\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) - 2\( \sqrt{7} \)
40\( \sqrt{7} \) - 2\( \sqrt{7} \)

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

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{10 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 4

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-8c⁵ x 3c⁵
(-8 x 3)c^{(5 + 5)}
-24c¹⁰

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.2km + 40.3km + 18.3km
total distance = 58.8km

By buying two shirts, Roger will save $18 x \( \frac{5}{100} \) = \( \frac{$18 x 5}{100} \) = \( \frac{$90}{100} \) = $0.90 on the second shirt.

So, his total cost will be
$18.00 + ($18.00 - $0.90)
$18.00 + $17.10
$35.10