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

\( \frac{14\sqrt{42}}{7\sqrt{6}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{42}{6}} \)
2 \( \sqrt{7} \)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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 $1,200
i = 0.08 x $1,200
i = $96

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

4\( \sqrt{18} \) - 7\( \sqrt{2} \)
4\( \sqrt{9 \times 2} \) - 7\( \sqrt{2} \)
4\( \sqrt{3^2 \times 2} \) - 7\( \sqrt{2} \)
(4)(3)\( \sqrt{2} \) - 7\( \sqrt{2} \)
12\( \sqrt{2} \) - 7\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61