9514 1404 393
Answer:
as written: (12√6)a²
Step-by-step explanation:
The way you have written this, only the numbers are under the radicals:
[tex]\sqrt{18}a^2\cdot4\sqrt{3}a^2=4\sqrt{18\cdot3}a^{2+2}=4\sqrt{3^2\cdot6}a^4\\\\=\boxed{12\sqrt{6}\cdot a^4}[/tex]
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We suspect you may want to simplify ...
[tex]\sqrt{18a^2}\cdot4\sqrt{3a^2}=4\sqrt{54a^4}=4\sqrt{6(3a^2)^2}=\boxed{12\sqrt{6}\cdot a^2}[/tex]
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We make use of the rules for combining radicals and exponents.
(√a)(√b) = √(ab)
(a^b)(a^c) = a^(b+c)
√(a²) = a . . . . for a ≥ 0
