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

7\( \sqrt{8} \) + 5\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) + 5\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) + 5\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) + 5\( \sqrt{2} \)
14\( \sqrt{2} \) + 5\( \sqrt{2} \)

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

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 $1,000
i = 0.07 x $1,000

No payments were made so the total amount due is the original amount + the accumulated interest:

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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.

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

\( \frac{2}{7} \) x \( \frac{1}{7} \) = \( \frac{2 x 1}{7 x 7} \) = \( \frac{2}{49} \) = \(\frac{2}{49}\)