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

3\( \sqrt{32} \) + 3\( \sqrt{2} \)
3\( \sqrt{16 \times 2} \) + 3\( \sqrt{2} \)
3\( \sqrt{4^2 \times 2} \) + 3\( \sqrt{2} \)
(3)(4)\( \sqrt{2} \) + 3\( \sqrt{2} \)
12\( \sqrt{2} \) + 3\( \sqrt{2} \)

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 $900
i = 0.09 x $900

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

To simplify a radical, factor out the perfect squares:

\( \sqrt{28} \)
\( \sqrt{4 \times 7} \)
\( \sqrt{2^2 \times 7} \)
2\( \sqrt{7} \)

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

8,770,000 in scientific notation is 8.77 x 10⁶

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.