How do you simplify square root of 4y^3 - square root y^3?

1 Answer
Sep 16, 2015

Answer:

#sqrt(4y^3) - sqrt(y^3)= y sqrt(y)#

Explanation:

The useful rule for square roots here is that #sqrt(ab) = sqrt(a)sqrt(b)#

This means that #sqrt(4y^3) = sqrt(4y^2y) = sqrt(4) sqrt(y^2) sqrt(y)#, which can be simplified to #2 y sqrt(y)#

#sqrt(y^3)# is similarly simplified to #sqrt(y^2y) = sqrt(y^2) sqrt(y) = ysqrt(y)#.

Subtracting the second from the first gives us
#2 y sqrt(y) - ysqrt(y) = ysqrt(y) #