To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{6} \) x 7\( \sqrt{8} \)
(5 x 7)\( \sqrt{6 \times 8} \)
35\( \sqrt{48} \)

Now we need to simplify the radical:

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

To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{3 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 2

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $700
i = 0.05 x $700
i = $35

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:

\( \sqrt{\frac{4}{25}} \)
\( \frac{\sqrt{4}}{\sqrt{25}} \)
\( \frac{\sqrt{2^2}}{\sqrt{5^2}} \)
\(\frac{2}{5}\)

Diane scored 93% on the test meaning she earned 93% of the possible points on the test. There were 200 possible points on the test so she earned 200 x 0.93 = 186 points. Each question is worth 2 points so she got \( \frac{186}{2} \) = 93 questions right.