To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{64}} \)
\( \frac{\sqrt{81}}{\sqrt{64}} \)
\( \frac{\sqrt{9^2}}{\sqrt{8^2}} \)
\( \frac{9}{8} \)
1\(\frac{1}{8}\)

To multiply terms with radicals, multiply the coefficients and radicands separately:

4\( \sqrt{8} \) x 5\( \sqrt{6} \)
(4 x 5)\( \sqrt{8 \times 6} \)
20\( \sqrt{48} \)

Now we need to simplify the radical:

20\( \sqrt{48} \)
20\( \sqrt{3 \times 16} \)
20\( \sqrt{3 \times 4^2} \)
(20)(4)\( \sqrt{3} \)
80\( \sqrt{3} \)

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

2 + (2 + 2) ÷ 4 x 5 - 3²
P: 2 + (4) ÷ 4 x 5 - 3²
E: 2 + 4 ÷ 4 x 5 - 9
MD: 2 + \( \frac{4}{4} \) x 5 - 9
MD: 2 + \( \frac{20}{4} \) - 9
AS: \( \frac{8}{4} \) + \( \frac{20}{4} \) - 9
AS: \( \frac{28}{4} \) - 9
AS: \( \frac{28 - 36}{4} \)
\( \frac{-8}{4} \)
-2

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 7}{5 x 7} \) - \( \frac{2 x 5}{7 x 5} \)

\( \frac{28}{35} \) - \( \frac{10}{35} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{28 - 10}{35} \) = \( \frac{18}{35} \) = \(\frac{18}{35}\)