How do you simplify the following radical expressions: \frac{\sqrt{72}}{\sqrt{36x^{8}y^{2}}}?

Layla-Rose Ellison

Layla-Rose Ellison

Answered question

2022-03-02

How do you simplify the following radical expressions: 7236x8y2?

Answer & Explanation

blokova5u8

blokova5u8

Beginner2022-03-03Added 7 answers

The notations a bit ambiguous, but what I think you’re asking about is 7236x8y2. So, the first thing we want to do is see what we can get outside the radicals. And right off the bat I’m seeing 62 in both the numerator and the denominator. Also, that y2 will reduce nicely. As will the x8, although not quite as far.
So, if you’re playing the home game and following along we now have 62262(x4)2y2. And you may be asking, why write it like that? To make it easier to see what I did next (though if you’re comfortable with exponents, you can skip right to this step)
So, two things to recall: xaxb=xab and x=x12. Applying both of those things is how we get to 626x4y then to 2x4y.
And there isn’t much more we can do here.
toeneepnla

toeneepnla

Beginner2022-03-04Added 4 answers

How do you simplify the following radical expressions: 7236x8y2?
Assuming 7236x8y2
7236x8y2=189x8y2 Note that y2= Absolute value(y)
183x4|y| Note that 18=92=32
323x4|y|=2x4|y|
For the case where all variable values represent non-negative quantities, we can write 2x4y

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