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

4\( \sqrt{112} \) - 3\( \sqrt{7} \)
4\( \sqrt{16 \times 7} \) - 3\( \sqrt{7} \)
4\( \sqrt{4^2 \times 7} \) - 3\( \sqrt{7} \)
(4)(4)\( \sqrt{7} \) - 3\( \sqrt{7} \)
16\( \sqrt{7} \) - 3\( \sqrt{7} \)

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

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

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:

\( \frac{3}{6} \) x \( \frac{4}{8} \) = \( \frac{3 x 4}{6 x 8} \) = \( \frac{12}{48} \) = \(\frac{1}{4}\)