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So, we've already discovered what surds are in this video,
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and how to calculate with them, in these videos.
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We're now going to look at the final piece of the surds puzzle at what rationalizing the denominator is.
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We know that the denominator is the bottom part of a fraction.
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So, have a look at these.
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What do you notice about those that are rationalized and those that aren't?
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Rationalizing the denominator is when we move a square root from the bottom, the denominator, to the top, the numerator.
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For a surd to be in its simplest form, the denominator cannot be irrational.
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It can't have a square root in its denominator.
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It's not wrong, it's just not considered the simplest form.
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Let's have a look at how we meet the root.
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Multiply both, the top and bottom, by the root.
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And we get one multiplied by root two, which equals root two,
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and root two multiplied by root two, which is two,
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because the rules of surds means that we do two times two, which is four, and the square root of four is two.
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You can check this yourself on your calculator.
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Type in one over root two,
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press equals and the calculator will rationalize it for you.
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But this won't get you marks in your exams.
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You've got to show the working, but do you use it just to check yourself!
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So, here is one for you to do.
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Rationalize this fraction.
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Don't worry about the three, leave it where it is in the denominator.
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Pause the video, give the question a go and click play when you're ready.
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Did you get it right?
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Five root seven over twenty-one.
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So, let's have a look at a trickier example.
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I'll do the first bit for you, to get you started.
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We need to multiply it by the whole of the denominator,
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but change the sign.
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So, think of expanding brackets and the difference of two squares .
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We would get a squared plus a b minus a b minus b squared.
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and the plus a b and minus a b would cancel each other out,
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leaving us with just a squared minus b squared.
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This is exactly what we want to do here.
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We want to cancel out the surds.
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So, expand the denominator brackets and what you get?
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Pause the video ,work it out and click play when you're ready.
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You should have got eleven.
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So, going back to the question, we can simplify by expanding brackets.
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And we get this: twelve plus three root five over eleven.
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So, give this question a go yourself.
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Pause the video, work out the answer and click play when you're ready.
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Did you get it right?
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So, there you have rationalizing the denominator,
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which is just a fancy way of saying "remove any square roots from the denominator".
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We have to do this to ensure that we fully simplified our surds.
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