Question

Distribute and simplify the radicals below. (√12)+6)(-√8-√2)

A) -18√2-6√6
B) -6√5-2√3
C) -6√5+2√3
D) 18√2+6√6

Answer 1

To distribute and simplify the given radical expression, we first express √12 and √8 in terms of their simplified radicals and then use the distributive property to multiply the terms. After simplifying, the result is -6√6 - 18√2, corresponding to option A. The correct answer is option a.

Step-by-step explanation:

To distribute and simplify the radicals (√12)+6)(-√8-√2), we need to apply the distributive property and then simplify the resulting radicals.

First, let's express the radicals √12 and √8 in terms of their prime factors:

• √12 = √(4⋅ 3) = √4 ⋅ √3 = 2√3
• -√8 = -√(4⋅ 2) = -√4 ⋅ √2 = -2√2

Now we replace √12 with 2√3 and -√8 with -2√2 and distribute:

1. (2√3 + 6)(-2√2 - √2)
2. = 2√3 ⋅ (-2√2) + 2√3 ⋅ (-√2) + 6 ⋅ (-2√2) + 6 ⋅ (-√2)
3. = -4 ⋅ √6 - 2√6 - 12√2 - 6√2
4. = -6√6 - 18√2

The simplified form of the expression is -6√6 - 18√2, which corresponds to option A: -18√2 - 6√6.