Question

Simplify, and remember to rationalize the denominator if needed. Show your work as much as you can for partial credit.
squre root 16a divided by square root 4b

Answer 1

First let's rewrite the top and bottom into a more helpful form:
\[\sqrt{16a} = \sqrt{16} \sqrt{a} = \sqrt{4}\sqrt{4}\sqrt{a}\]

\[\sqrt{4b} = \sqrt{4} \sqrt{b}\]

so:

\[\sqrt{16a} / \sqrt{4b} = (\sqrt{4}\sqrt{4}\sqrt{a})/ (\sqrt{4}\sqrt{b})\]

You see how one of the square root 4 cancels out from the top and bottom:

\[= \sqrt{4}\sqrt{a} /\sqrt{b}\]

Now to rationalize the denominator, we should multiply the top and bottom by square root b.

\[(\sqrt{4}\sqrt{a} / \sqrt{b}) * (\sqrt{b}/\sqrt{b}) = (\sqrt{4}\sqrt{a}\sqrt{b}) / b = \sqrt{4ab}/b\]

Answer 2

thank you i guessed on it because i thought noone would help me