How do you simplify #sqrt((32a^4)/b^2)#?

Question

1947 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-08T13:38:40

See the solution process below:

We can rewrite this expression as:

#sqrt(((16 * 2)a^4)/b^2) => sqrt((16a^4)/b^2 * 2)#

Using this rule for radicals we can further rewrite this expression as:

#sqrt(a * b) = sqrt(a) * sqrt(b)#

#sqrt((16a^4)/b^2 * 2) => sqrt((16a^4)/b^2) * sqrt(2)#

We can now take the square root of the left radical to simplify this expression as:

#(+-4a^2)/bsqrt(2)#

Or, because the original question is given with only the principal root indicated:

#(4a^2)/bsqrt(2)#