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

7\( \sqrt{32} \) - 4\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) - 4\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) - 4\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) - 4\( \sqrt{2} \)
28\( \sqrt{2} \) - 4\( \sqrt{2} \)

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

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 terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

7b⁶ x 4b⁴
(7 x 4)b^{(6 + 4)}
28b¹⁰

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (4 + 2) ÷ 4 x 2 - 2²
P: 3 + (6) ÷ 4 x 2 - 2²
E: 3 + 6 ÷ 4 x 2 - 4
MD: 3 + \( \frac{6}{4} \) x 2 - 4
MD: 3 + \( \frac{12}{4} \) - 4
AS: \( \frac{12}{4} \) + \( \frac{12}{4} \) - 4
AS: \( \frac{24}{4} \) - 4
AS: \( \frac{24 - 16}{4} \)
\( \frac{8}{4} \)
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