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

4\( \sqrt{48} \) - 2\( \sqrt{3} \)
4\( \sqrt{16 \times 3} \) - 2\( \sqrt{3} \)
4\( \sqrt{4^2 \times 3} \) - 2\( \sqrt{3} \)
(4)(4)\( \sqrt{3} \) - 2\( \sqrt{3} \)
16\( \sqrt{3} \) - 2\( \sqrt{3} \)

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

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 42 meters so the equation becomes: 2w + 2h = 42.

Putting these two equations together and solving for width (w):

2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7

Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m²

The greatest common factor (GCF) is the greatest factor that divides two integers.

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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 20.7km + 8.5km
total distance = 29.6km

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

6\( \sqrt{175} \) + 8\( \sqrt{7} \)
6\( \sqrt{25 \times 7} \) + 8\( \sqrt{7} \)
6\( \sqrt{5^2 \times 7} \) + 8\( \sqrt{7} \)
(6)(5)\( \sqrt{7} \) + 8\( \sqrt{7} \)
30\( \sqrt{7} \) + 8\( \sqrt{7} \)

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