Question

How do you simplify `sqrt(4c^3d^3)*sqrt(8c^3d)`?

Answer 1

`4sqrt(2)c^3d^2`

Explanation:

Supposing that everything is well defined:

`sqrt(4c^3d^3)sqrt(8c^3d)=sqrt(2^{2+3}c^{3+3}d^{3+1})=2^{5/2}c^{6/2}d^{4/2}=4sqrt(2)c^3d^2`

Answer 2

See the solution process below:

Explanation:

We can use this rule for multiplying radicals to rewrite the expression:

`sqrt(a) * sqrt(b) = sqrt(a * b)`

`sqrt(4c^3d^3) * sqrt(8c^3d) = sqrt(4c^3d^3 * 8c^3d) = sqrt(32c^3c^3d^3d)`

We can use these rules for exponents to rewrite the `c` and `d` terms:

`a = a^color(red)(1)` and `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`sqrt(32c^3c^3d^3d) = sqrt(32c^color(red)(3)c^color(blue)(3)d^color(red)(3)d^color(blue)(1)) = sqrt(32c^(color(red)(3)+color(blue)(3))d^(color(red)(3)+color(blue)(1))) = sqrt(32c^6d^4)`

We can now rewrite the expression and take the square root of terms:

`sqrt(32c^6d^4) = sqrt(2 * (16c^6d^4)) = sqrt(2) * sqrt(16c^6d^4) = sqrt(2) * +-4c^3d^2 = +-4sqrt(2)c^3d^2`