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.

√6 (4√6 - 3√2)

Accepted Answer

Hello, everyone. For the following expression, we are going to perform multiplication and further simplify if possible. The expression we're given is radical 15, multiplied by the quan D 8 Radical 15 -7 Radical 5. Our answer choices are a 35 radical 3 - B 120 Radical 3 -35 c 35 -120 Radical D 120 -35 Radical 3, rewriting my original expression. I have radical and that's multiplied by the quantity 8 radical 15 -7 radical 5. So even though we have square root symbols also known as radicals in this problem, we are going to treat it just like any other distribution multiplication problem. So I'm gonna start out by multiplying radical 15 x 8 radical 15. Recall that when you multiply radicals, it's kind of like multiplying variables. You can multiply what's under the radical and the radical stays, our coefficient of eight does not change. So this will be eight radical and then 15 times 15 is the same as 15 squared. So if we have eight multiplied by the square of 15 squared and then I can do the square to 15 multiplied by -7 radical 5. So similarly, the -7 stays put. I can multiply what is under my square root symbols. So I keep the radical sign and I can do five multiplied by 15, which is 75. So next, I'm gonna simplify what I can. The first thing I see that I can simplify is I can take the square root of 15 squared. So the coefficient of eight stays put and that's gonna be multiplied by the square root of 15 squared, which is 15. Next, I'm gonna see if I can simplify anything with the -7 radical 75. So -7 is Gonna stay put. I recall that when I'm working with square roots, I can break them down, meaning I can try to find a perfect square that I can take out of there. So 75, I could break that down to the square root of three multiplied by the square root of 25. I do this because the square of 25 is 5. So in my next step, simplifying this a little bit more, eight times 15 or eight multiplied by 15 is 120 minus seven. And we're gonna multiply that by the squared of 15 or sorry, the squared of 25 which is five multiplied by the squared of three. So I now have -7 times 5 is 35 radical 3. That is my solution and it is answer choice. D have a nice day.

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)

Key Concepts

Radical Expressions

Distributive Property

Simplifying Radical Expressions

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