Homework Help

Simplify. `sqrt((25x^2y)/(75xy^5))` 

user profile pic

kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted April 19, 2013 at 2:31 PM via web

dislike 2 like



2 Answers | Add Yours

user profile pic

oldnick | (Level 1) Valedictorian

Posted April 19, 2013 at 2:38 PM (Answer #1)

dislike 1 like

`sqrt((25x^2y)/(75xy^5))=sqrt((25/75)(x^2/x)(y/y^5))=` `sqrt(1/3xy^(-4))` `=sqrt(1/3x/y^4)` `=sqrt(3)/(3y^2)sqrt(x)`

user profile pic

mjripalda | High School Teacher | (Level 1) Senior Educator

Posted April 19, 2013 at 3:13 PM (Answer #2)

dislike 1 like


To simplify this expression, reduce the fraction 25/75 to its lowest term.


Then, to divide same variables, apply this property of exponents which is `a^m/a^n=a^(m-n)` .


For negative exponent, use `a^(-m)=1/a^m` .


Then, apply this property of radicals which is `root(n)(a/b)=root(n)(a)/root(n)(b)` .


Note that `root(m)(a^m)=a` . So,

`=sqrt(x)/sqrt(3y^2*y^2)= sqrt(x)/(y*ysqrt3)=sqrt(x)/(y^2sqrt3)`

To simplify further, rationalize the denominator. 


Since `sqrta*sqrta=a` , then:


In multiplying radicals with same index, apply this property `root(n)(a)*root(n)(b)=root(n)(a*b)` .


Hence, `sqrt((25x^2y)/(75xy^5))=sqrt(3x)/(3y^2)` .

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes