SOLUTION: 3 ∜ 24 multiplied by 5 ∜ 2 why is the answer 30 ∜3

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Question 395159: 3 ∜ 24
multiplied by
5 ∜ 2
why is the answer 30 ∜3
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

This is all multiplication. So we can use the Commutative and Associative Properties to rearrange the order and grouping in any way we choose:

To multiply the radicals we use the property of all radicals: :

or

Just like fractions should be reduced, radicals should be simplified. Simplifying radicals involves finding factors of the radicand (the expression within a radical) that are powers of the type of root, if any. In this problem with its 4th root, we are looking for factors of 48 that are a power of 4. Since and since 16 is a factor of 48, this radical will simplify. We start by writing the radicand in factored form:

Then we use the property of radicals we used earlier. Only this time we use it in the other direction: to split a single radical into a product of radicals. By doing this we get the power of 4 factor into its own radical:

The 4th root of 16 is 2 so this becomes:

which simplifies to
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