How do you simplify # sqrt(320y^2)#?

1 Answer
Apr 30, 2016

Answer:

#sqrt(320y^2) = 8sqrt(5)abs(y)#

Explanation:

If #a, b >= 0# then #sqrt(ab) = sqrt(a)sqrt(b)#

In our example, we know that #y^2 = abs(y)^2 >= 0#

In addition note that #320 = 64*5 = 8^2*5#

So:

#sqrt(320y^2) = sqrt(8^2*5*abs(y)^2) = sqrt(8^2)*sqrt(5)*sqrt(abs(y)^2) = 8sqrt(5)abs(y)#