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PH Algebra I - Lesson 11.6 Problem 57

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  • Mrs Bee
    replied
    This is funny, Cindy in Indy ... in a way. So he went full circle, and I didn't see that. The book says a factored form is the simplest form, so that's where the origin of all this might be. You have factors, you multiply them, but then factor the product and you get what you had at the beginning... unsurprisingly! Ah well, it's all good practice.

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  • Cindy in Indy
    replied
    I mentioned your question to my colleague, who teaches algebra2. She pointed out that the factored answer your son got is actually the first step in the rationalizing process. Then he simplified the denominator, but the numerator is still factored. He took two extra steps to multiply it out and then factor it again.

    She also mentioned that in calculus, they sometimes rationalize the numerator. That might be a fun challenge problem for your kiddos.

    Kind regards.

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  • Mrs Bee
    replied
    Dear Cindy in Indy , what a sweet reply! I am relieved I can tell my kids they are both right - it doesn't happen often!! But if I took down points for squabbling, nobody would ever get nice grades around here!

    I sided with my son because we have all internalized that the book wants answers at their lowest terms, whatever that might mean in each case. When I saw that my son was able to tease out so much more, I thought the book perhaps had printed not the final solution, but an intermediate step. It's a grave sin in this house to think you've arrived at the answer when you're still a few steps away from it

    My son tends to have an intuitive understanding of math I admire very much, but he still makes his fair share of "Duh!" mistakes

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  • Cindy in Indy
    replied
    Hi Mrs. Bee,

    I must admit, I would have gotten the same answer as your daughter. Your son, however, noticed a further simplification that most people would not see (including the authors of the book). His answer is also correct. Depending on the purpose of this math problem, your daughter's answer might be more useful in some situations. Your son's answer is perhaps more "elegant". Has he considered a future in mathematics? That's the way a mathematician thinks!

    Anyway, they are both correct. They may be docked 2 points for squabbling, however

    Good work to both! This problem is in the challenge section, and many algebra1 students would not have gotten the correct answer.

    Kudos to you for patiently typing out both answers and the methodology. You are doing well, momma!

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  • Mrs Bee
    started a topic PH Algebra I - Lesson 11.6 Problem 57

    PH Algebra I - Lesson 11.6 Problem 57

    My kids are squabbling over this.

    My girl gave the same answer as the Solution Key, which is 24+8*(square root of 2)+3*(square root of 3)+(square root of 6), everything over 7.

    My son was bothered by that square root of 6 left untouched, and factored it as (square root of 2)*(square root of 3). Then he factored that whole numerator by grouping: he factored 8 out of the first two terms, so he got 8*(3+square root of 2), then he factored the square root of 3 out of the other two terms, and he got (square root of 3)*(3+square root of 2). Then he factored (3+square root of 2), and his final answer was as follows: (3+square root of 2)(8+square root of 3), everything over 7.

    I'm siding with my son. Who's right?

    Thank you!
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