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

3 + (2 + 3) ÷ 3 x 2 - 5²
P: 3 + (5) ÷ 3 x 2 - 5²
E: 3 + 5 ÷ 3 x 2 - 25
MD: 3 + \( \frac{5}{3} \) x 2 - 25
MD: 3 + \( \frac{10}{3} \) - 25
AS: \( \frac{9}{3} \) + \( \frac{10}{3} \) - 25
AS: \( \frac{19}{3} \) - 25
AS: \( \frac{19 - 75}{3} \)
\( \frac{-56}{3} \)
-18\(\frac{2}{3}\)

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

6\( \sqrt{63} \) + 6\( \sqrt{7} \)
6\( \sqrt{9 \times 7} \) + 6\( \sqrt{7} \)
6\( \sqrt{3^2 \times 7} \) + 6\( \sqrt{7} \)
(6)(3)\( \sqrt{7} \) + 6\( \sqrt{7} \)
18\( \sqrt{7} \) + 6\( \sqrt{7} \)

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:

\( \sqrt{\frac{64}{81}} \)
\( \frac{\sqrt{64}}{\sqrt{81}} \)
\( \frac{\sqrt{8^2}}{\sqrt{9^2}} \)
\(\frac{8}{9}\)

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

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{10 + 2 + 7 + 5}{4} \) = \( \frac{24}{4} \) = 6