Question

Multiply. Assume p, q, and r are greater than or equal to zero, and write your answer in the simplest form.

radical 11p^4 q^3 r · 2 radical 385p^4 r

Answer 1

`{22p^4qr\sqrt{35q`

Explanation:

I am interpreting what you wrote as
`√(11p^4q^3r) \cdot2√(385p^4r)`, sorry if that's not what you meant!

We rewrite
`385` as
`5 \cdot 7 \cdot 11`. Since the radicals have the same index, the expression can be written as

`√(11p^4q^3r) \cdot2√(385p^4r)=2√(11p^4q^3r\cdot5\cdot7\cdot11p^4r)`.

Multiplying like terms, the expression simplifies to

`2√(5\cdot7\cdot11^2p^8q^3r^2)\\`.

Taking out the perfect square factors,
`11^2, p^8, q^2,` and
`r^2,` we get

`2\cdot11p^4qr\sqrt{5\cdot7q`, or

`\boxed{22p^4qr√(35q)}`.

`\begin{align*}\\√(11p^4q^3r) \cdot√(385p^4r)=√(11p^4q^3r\cdot5\cdot7\cdot11p^4r)\\=√(11^2p^8q^3r^2)\\\end{align*}`
`\begin{align*}√(5*4)\\\end{align*}`