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:

\( \sqrt{\frac{49}{64}} \)
\( \frac{\sqrt{49}}{\sqrt{64}} \)
\( \frac{\sqrt{7^2}}{\sqrt{8^2}} \)
\(\frac{7}{8}\)

Diane scored 90% on the test meaning she earned 90% of the possible points on the test. There were 360 possible points on the test so she earned 360 x 0.9 = 324 points. Each question is worth 4 points so she got \( \frac{324}{4} \) = 81 questions right.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 4h \)
240 miles

1

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).