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    Do we NEED the square roots to cancel out as demonstrated in the mini question explanation?

    Module 2 Day 13 Challenge Part 3
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    • The Blade DancerT
      The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
      last edited by debbie

      Module 2 Week 4 Day 13 Challenge Part 3

      Do we NEED the square roots to cancel out as demonstrated in the mini question explanation?

      The Blade Dancer
      League of Legends, Valorant: Harlem Charades (#NA1)
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      debbieD 1 Reply Last reply Reply Quote 3
      • debbieD
        debbie ADMIN M0★ M1 M5 @The Blade Dancer
        last edited by debbie

        @TSS-Graviser Hi again!

        You have a good point! If you're just in the middle of a calculation, and you get a fraction with a radical in the denominator, but it's only an intermediate step, you don't really have to take out the square root from the bottom. It's just for you to look at, right?

        $$ \frac{2}{\sqrt{5} - 1} $$

        cartoon-po-happier-30-percent.jpg
        "I would probably leave it like that." -- Prof. Loh
         

        However, if your final answer has a square root in the bottom of the fraction, I'd recommend simplifying to remove it. This is called "rationalizing the denominator." It's perhaps easier for teachers to check students' answers if they all are in the same format.

        Like, imagine if you were a teacher, and your students gave you answers that looked like:

        $$ \frac{1}{2+1}, \text{ } \frac{3-2}{4-1}, \text{ } \frac{0.5}{1.5}, \text{ and } \frac{5}{15}$$

        These are all equal to \(\frac{1}{3},\) but it wouldn't be a lot of fun to check that!

        The reason might be just due to convention, but there are some discussions on other websites explaining that, to name a reason, it's easier to add fractions when their denominators are integers. For example, it's easier to add

        $$ \frac{\sqrt{3}}{3} + \frac{\sqrt{6}-\sqrt{3}}{3} $$

        compared with adding

        $$ \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{6}}. $$

        cartoon-po-happier-30-percent.jpg

        "That's ugly!" says Prof. Loh

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