How do you simplify # sqrt ( 9 /( 50xy^7))#?

1 Answer
Jul 18, 2017

Answer:

#= (3sqrt(2xy))/(10xy^4#

Explanation:

Write the numbers as a product of their factors, using squares where possible.

Find roots where possible.

#sqrt(9/(50xy^7)) " "= sqrt((3xx3)/(2xx5xx5 x y y^6)#

#=3/(5y^3)sqrt(1/(2xy))" " =3/(5y^3)1/(sqrt(2xy)) " "= 3/(5y^3sqrt(2xy))#

You will probably want to rationalise the denominator

#3/(5y^3sqrt(2xy)) xx sqrt(2xy)/sqrt(2xy)#

#=(3sqrt(2xy))/(5y^3 xx 2xy)#

#= (3sqrt(2xy))/(10xy^4#