In Exercises 1–38, multiply as indicated. If possible, simplify a...

Question

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.

³√3 (³√6 + 7 ³√4)

Accepted Answer

Hello everyone. For the following expression, we are going to perform multiplication and further simplify if possible. The expression we have is the cube root of seven multiplied by the quantity the cube root of two plus nine cube root of 11. Our answer choices are a, the cube root of 14 plus nine cube root of B. The cube root of 14 plus nine cuber of C three cube root of 14 plus the cube root of 77 D three cu root of 14 plus the cube root of 22. I'm gonna rewrite my original expression. So the cube root of seven multiplied by the quan D the cube root of two plus nine cube root of 11. So I recall that in this circumstance, we start out solving this just like any other distribution multiplication problem. I'm gonna take the value that's on the outside of the parentheses and multiply it by each term on the inside of the parentheses. So the cube root of seven multiplied by the cube root of two. Recall that when we multiply radicals that have the same index, the little cube root, we keep the radical and we multiply what's underneath. So in this case, we keep this the cube root and seven multiplied by 2 is 14. Next, we have the cub root of seven multiplied by nine cube root of 11. Again, very much like when we have variables nine is like our coefficient, there's nothing to multiply it by that will change it. So it stays nine and then the cube root of seven multiplied by the cube root of 11 will give us still the cube root seven multiplied by 11 is 77. Next I stop and see if there's anything else I can simplify. Here is 14, a perfect cube route. Is there a cube route I can take out of 14? There is not same with 77. 77 is not a perfect cube route. I can't think of a cube that I can factor out of it. So this is our solution cuber to 14 plus nine cuber to 77. That's answer choice. A have a nice day.

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. ³√3 (³√6 + 7 ³√4)

Key Concepts

Radical Expressions

Distributive Property

Simplifying Radicals

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