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4 votes
Simplify the radical:

√(5x^4)/
√(10x)

User JonLuca
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1 Answer

3 votes
Split up the top and bottom into factors and cancel out any common factors.

While we do these problems, it is important to remember this rule:


√(ab) = √(a) √(b)

First, we will split up the top.


√(5x^4) = √(5) √(x^4)

We can't do anything with the square root of 5 because it is in it's simplest form. But, we can still split up the square root of
x^2


√(5) √(x^4) = √(5) √(x^2) √(x^2)

Now we can simplify.


√(5) √(x^2) √(x^2) = √(5) x * x


√(5) x * x = √(5)x^2

The top is done, now for the bottom one.


√(10x) = √(10) √(x)

We can't simplify either the square root of 10 or the square root of x.
So, the top is done, too.

Find any common factors and cancel them out.


(√(5)x^2)/(√(10) √(x))

Well, I can't find any common factors to cancel out, but, we can still simplify it further.

There is another law regarding radical expressions:


\sqrt{(a)/(b)} = (√(a))/(√(b))

Using this, simplify the expression further.


(√(5)x^2)/(√(10) √(x)) = \sqrt{(5)/(10)} (x^2)/(√(x))


\sqrt{(5)/(10)} (x^2)/(√(x)) = \sqrt{(1)/(2)} (x^2)/(√(x))

So, now it is in it's simplest form.
User Nknj
by
8.1k points

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