Question

Multiply.

43√⋅1012−−√⋅6√⋅2√



Enter your answer, in simplest radical form, in the box.
(Picture of the equation just in case it copied it wrong)

Answer 1

Answer: Esta es la respuesta correcta

Explanation:

Answer 2

The main rules that we use here are :

i)
`√(a \cdot b)= √(a) \cdot √(b)` for nonnegative values a and b.

ii)
`√(a) \cdot √(a) =a`.


Thus, first 'decompose' the numbers in the radicals into prime factors:


`4 √(3) \cdot 10 \cdot √(2\cdot2\cdot3)\cdot √(2\cdot 3)\cdot √(2).`.

By rule (i) we write:


`4 √(3) \cdot 10 \cdot √(2)\cdot √(2)\cdot √(\cdot3)\cdot √(2) \cdot √(3) \cdot √(2)`.

We can collect these terms as follows:


`40 √(3)\cdot (√(3)\cdot √(3)) \cdot (√(2)\cdot √(2)) \cdot( √(2) \cdot √(2))`, and by rule (ii) we have:


`40 √(3)\cdot 3 \cdot 2 \cdot2=40\cdot12\cdot √(3)=480 √(3).`


Answer:
`480 √(3)`.