To simplify a radical, factor out the perfect squares:

\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)

The amount of flour you need is (2\(\frac{7}{8}\) - 1\(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{23}{8} \) - \( \frac{13}{8} \)) cups
\( \frac{10}{8} \) cups
1\(\frac{1}{4}\) cups

Latoya scored 83% on the test meaning she earned 83% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.83 = 100 points. Each question is worth 4 points so she got \( \frac{100}{4} \) = 25 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 6 meters so the equation becomes: 2w + 2h = 6.

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

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

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

\( \frac{4}{6} \) x \( \frac{1}{6} \) = \( \frac{4 x 1}{6 x 6} \) = \( \frac{4}{36} \) = \(\frac{1}{9}\)