How do you simplify #\sqrt { 6x y ^ { 18} }#?

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Answer 1 · 2017-09-13T09:31:21

# y^9sqrt(6x)#

We need to factor the radicand (the value in the root symbol ) in a way that allows us to extract any roots. This can be done as follows:

#sqrt( 6xy^18)# can be factored as #sqrt( 6 * x * y^18 )#

Notice that #y^9 * y^9 = y^18# . This implies that #y^9# is the square root of #y^18# so this can be removed from the radicand:

#y^9sqrt( 6 * x )#

Neither #6# nor #x# can be factored to give any exact roots, so this is as far as we can go.

Result is:

# y^9sqrt(6x)#