WEBVTT
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Simplify the following expression.
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The square root of 75 plus
the square root of 48.
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These types of questions can
sometimes be intimidating
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because the numbers may not
look immediately familiar to us.
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We think we don't know
the square root of 75,
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or we don't know the square root of 48,
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especially these kind of bigger numbers.
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But often when you see that
really what it's testing
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is your ability to understand
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that the square root of
75 or 48 essentially,
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can kind of be broken down
or you kind of understand
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its component parts and simplify it
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into numbers that we're
much more familiar with.
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So for example, if it said
the square root of 25,
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that would be much more
readily identifiable
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as five essentially.
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But once we start working
with these numbers
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or know a little bit about them,
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we'll see that breaking them
into their parts essentially,
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in order to simplify them,
or in able to work with them,
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isn't too difficult.
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So in this example, we can say
that the square root of 75.
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Let's work with that one first.
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We would recognize that 75
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is equivalent to 25 times three.
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So that's the kind of
thing we're looking for.
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We're kind of looking for
squares that we would recognize
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as factors of this number.
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So we could say that 75 is equal to
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five times five, 25, times three.
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If we have the square root
of a number being squared
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essentially we can just take this out.
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So that becomes five times
the square root of three.
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So the square root of 75 is the same
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as five times the square root of 3.
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That's kind of the important
part to understand.
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Similarly, of course, for
the square root of 48,
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we might recognize that
the square root of 48
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could be expressed as
four times four times,
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square root of four
times four times three.
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And again we're doing the same thing,
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we can take that four out
since we have a perfect square.
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Square root of 48 is equal to
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four times the square root of three.
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Now of course you could
calculate these out
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to decimal points or something like that
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but for our purposes, these
are in simple enough form
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to work with and most likely,
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some of the things that
you would see on the test
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would be kind of like this.
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You would keep it in this form.
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So now, instead of square
root 75 plus square root 48,
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essentially now you're saying
five square root of three
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plus four times the square root of three.
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So if you have some number of a thing
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and you have another
number of that same thing,
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you could just add them
together, of course.
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That means that this is equal to nine.
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Five of these, plus four of these,
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makes nine of these.
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Of these, meaning square
root threes essentially.
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So nine times the square root of three.
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So we've now simplified square root 75
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plus the square root 48
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into nine square root of three.
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And that would be the form
required in this answer.
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So we see that that is answer choice D.