Question

Multiply. 3√2⋅2√8⋅√3⋅√6

explanation would be lit

Answer 1

72√2

Explanation:

simplify all of the radicals into their factors, then pull out integers. If you do this, only √2 remains. Then, multiply all the integers.

Answer 2

When two the same numbers under the square root multiply, they are equal to the value under the square root, for example √2⋅√2 = 2. So then we have:

3√2⋅2√8⋅√3⋅√6 = 3⋅√2⋅2⋅√(2⋅2⋅2)⋅√3⋅√(3⋅2) = 3⋅2⋅√2⋅√2⋅√2⋅√2⋅√2⋅√3⋅√3 = 3⋅2⋅2⋅√2⋅3 = 36⋅√2

or if the bolded 2 from above is also the square root, then the solution is:

3√(2⋅2)√(2⋅2⋅2)⋅√3⋅√(3⋅2) = 54