Final Answer:
$2\sqrt{12}$, $-6x\sqrt{2}$, $-4\sqrt{5}$, $28t\sqrt{2}$, $-2\sqrt{6}$, $4w\sqrt{5}$, $-2\sqrt{35}$, $-4\sqrt{5v}$
Wait — that’s not simplified correctly. Let me recompute each one carefully and give only the *fully simplified* final answers.
We simplify each product using $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$, and factor out perfect squares.
1. $\sqrt{8} \cdot \sqrt{6} = \sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$
2. $-\sqrt{2x} \cdot \sqrt{18x} = -\sqrt{36x^2} = -6|x|$, but since radicals assume nonnegative variables in basic algebra, we write $-6x$
3. $-\sqrt{20} \cdot -\sqrt{4} = (+)\sqrt{80} = \sqrt{16 \cdot 5} = 4\sqrt{5}$
4. $\sqrt{4t} \cdot 7\sqrt{8t} = 7 \cdot \sqrt{32t^2} = 7 \cdot \sqrt{16 \cdot 2 \cdot t^2} = 7 \cdot 4t\sqrt{2} = 28t\sqrt{2}$
5. $-\sqrt{3} \cdot \sqrt{8} = -\sqrt{24} = -\sqrt{4 \cdot 6} = -2\sqrt{6}$
6. $w\sqrt{80} \cdot \sqrt{4} = w \cdot \sqrt{320} = w \cdot \sqrt{64 \cdot 5} = w \cdot 8\sqrt{5} = 8w\sqrt{5}$
7. $\sqrt{7} \cdot -\sqrt{20} = -\sqrt{140} = -\sqrt{4 \cdot 35} = -2\sqrt{35}$
8. $-\sqrt{8} \cdot -\sqrt{10v} = +\sqrt{80v} = \sqrt{16 \cdot 5v} = 4\sqrt{5v}$
Now list only the simplified answers in order (left column top to bottom, then right column top to bottom):
Final Answer:
$4\sqrt{3}$, $-6x$, $4\sqrt{5}$, $28t\sqrt{2}$, $-2\sqrt{6}$, $8w\sqrt{5}$, $-2\sqrt{35}$, $4\sqrt{5v}$
Parent Tip: Review the logic above to help your child master the concept of multiplying and dividing radicals worksheet.
