Answer:
14. -5√30 +3√2
15. 18√5 -30√3
Step-by-step explanation:
You can multiply radicals using ...
(√a)(√b) = √(ab)
And you can simplify radicals using ...
√(a²b) = a√b
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14. Using the distributive property, then simplifying the radicals, we have ...
[tex]\sqrt{3}(-5\sqrt{10}+\sqrt{6})\\\\=-5\sqrt{3\cdot10}+\sqrt{3\cdot6}\\\\=-5\sqrt{30}+\sqrt{3^2\cdot2}\\\\=\boxed{-5\sqrt{30}+3\sqrt{2}}[/tex]
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15. Similarly, ...
[tex]-2\sqrt{15}(-3\sqrt{3}+3\sqrt{5})\\\\=6\sqrt{15\cdot3}-6\sqrt{15\cdot5}\\\\=6\sqrt{3^2\cdot5}-6\sqrt{5^2\cdot3}\\\\=\boxed{18\sqrt{5}-30\sqrt{3}}[/tex]
