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:

\( \sqrt{\frac{9}{9}} \)
\( \frac{\sqrt{9}}{\sqrt{9}} \)
\( \frac{\sqrt{3^2}}{\sqrt{3^2}} \)
1

To simplify a radical, factor out the perfect squares:

\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)

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

2\( \sqrt{45} \) + 2\( \sqrt{5} \)
2\( \sqrt{9 \times 5} \) + 2\( \sqrt{5} \)
2\( \sqrt{3^2 \times 5} \) + 2\( \sqrt{5} \)
(2)(3)\( \sqrt{5} \) + 2\( \sqrt{5} \)
6\( \sqrt{5} \) + 2\( \sqrt{5} \)

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

April scored 95% on the test meaning she earned 95% of the possible points on the test. There were 240 possible points on the test so she earned 240 x 0.95 = 228 points. Each question is worth 3 points so she got \( \frac{228}{3} \) = 76 questions right.

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 48 meters so the equation becomes: 2w + 2h = 48.

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

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

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

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²