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

2\( \sqrt{27} \) - 8\( \sqrt{3} \)
2\( \sqrt{9 \times 3} \) - 8\( \sqrt{3} \)
2\( \sqrt{3^2 \times 3} \) - 8\( \sqrt{3} \)
(2)(3)\( \sqrt{3} \) - 8\( \sqrt{3} \)
6\( \sqrt{3} \) - 8\( \sqrt{3} \)

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

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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

5 + (5 + 2) ÷ 4 x 2 - 3²
P: 5 + (7) ÷ 4 x 2 - 3²
E: 5 + 7 ÷ 4 x 2 - 9
MD: 5 + \( \frac{7}{4} \) x 2 - 9
MD: 5 + \( \frac{14}{4} \) - 9
AS: \( \frac{20}{4} \) + \( \frac{14}{4} \) - 9
AS: \( \frac{34}{4} \) - 9
AS: \( \frac{34 - 36}{4} \)
\( \frac{-2}{4} \)
-\(\frac{1}{2}\)

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