To simplify a radical, factor out the perfect squares:

\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)

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 first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

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

4 + (5 + 4) ÷ 3 x 4 - 5²
P: 4 + (9) ÷ 3 x 4 - 5²
E: 4 + 9 ÷ 3 x 4 - 25
MD: 4 + \( \frac{9}{3} \) x 4 - 25
MD: 4 + \( \frac{36}{3} \) - 25
AS: \( \frac{12}{3} \) + \( \frac{36}{3} \) - 25
AS: \( \frac{48}{3} \) - 25
AS: \( \frac{48 - 75}{3} \)
\( \frac{-27}{3} \)
-9