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Simplify fully one plus root two times four minus root two, giving your answer in the form š¯‘ˇ plus š¯‘¸ root two, where š¯‘ˇ and š¯‘¸ are integers.
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So what theyā€™re telling you to do basically is multiply these brackets together.
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And weā€™ve just seen an example of that using the FOIL method, but theyā€™re asking for the answer in a very specific format.
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And they do intend to throw these kinds of little twists into trying to throw you off the sense sometimes.
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š¯‘ˇ plus š¯‘¸ root two, so this just means an integer ā€” so a whole number ā€” plus some whole number times the square root of two.
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So theyā€™re not asking you for the value of š¯‘ˇ or š¯‘¸ particularly, theyā€™re just asking you to represent your answer in that kind of layout.
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Okay, letā€™s write out the question and stop multiplying out the brackets.
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So weā€™re gonna do one times four, which gives us four.
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Weā€™re then gonna do one lot of negative root two, which is just negative root two.
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Then root two times four or four lots of root two, theyā€™re both positive number; so itā€™s gonna be a positive answer.
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And then weā€™ve got positive root two times negative root two.
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So positive times negative is gonna give us a negative answer and then weā€™ve got root two times root two.
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So I just really need that for the moment, but we do know that root two times root two as we just saw is just two.
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So weā€™ve got four take away two in terms of just normal rational numbers, and four take away two is two.
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And then weā€™re starting off with negative root two.
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Well that really means thereā€™s just one of them.
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So itā€™s really negative one root two, one lot of root two.
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And then weā€™re adding another four lots of root two.
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So if we start off a negative one on the number line and add four, weā€™re gonna go one, two, three, four steps up to positive three.
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So hereā€™s our answer then, two plus three root two.
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And this tallies with the format that weā€™ve been asked to give the answer in.
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So in this case, š¯‘ˇ would be two and š¯‘¸ is the multiplier of the root two here would be equal to three.
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Just check the signs carefully.
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So we were asked for š¯‘ˇ plus š¯‘¸ root two.
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Well weā€™ve got two plus three root two.
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So we know that š¯‘ˇ will be two and š¯‘¸ will be three.
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As I said before, they didnā€™t actually ask for the value of š¯‘ˇ and š¯‘¸.
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But in some questions, they do; so at least you now know how to answer those sorts of questions as well.