How do you simplify #\frac { \sqrt { 135x ^ { 10} } } { \sqrt { 5x } }#?

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Answer 1 · 2017-08-02T14:52:58

#3x^4sqrt(3x)#

We can also write this as a fraction under a single radical:

#sqrt((135x^10)/(5x))#

No we simplify the fraction algebraically, leaving us with

#sqrt(27x^9#

The prime factorization of #27# is

#27 = underbrace(3*3)_1*3#

So we can leave one #3# outside and one inside:

#3sqrt(3x^9)#

Now we can see groups of #2# of #x^9#:

#underbrace(x*x)_1*underbrace(x*x)_2*underbrace(x*x)_3*underbrace(x*x)_4*x#

We can thus leave an #x^4# outside and a single #x# inside the radical:

#> color(blue)(ulbar(|stackrel(" ")(" "3x^4sqrt(3x)" ")|)#