## ahoymewmew 3 years ago Can someone help me with Multiplying Radicals?

1. ahoymewmew

These are the problems. V

2. wio

Where are you stuck? Do you know: $\sqrt{a}\times \sqrt{b} = \sqrt{a\times b}$

3. ahoymewmew

no @wio its confusing me.

4. CliffSedge

Multiply the numbers that are outside the radicals together, then multiply the numbers inside the radicals together. If the new radicand can be simplified by extracting roots, then do that and multiply those roots by the numbers outside.

5. CliffSedge

#3 as an example: $7xy \sqrt{2x} \cdot 3\sqrt{4xy^2} \rightarrow (7xy)(3) \cdot \sqrt{(2x)(4xy^2)}$

6. CliffSedge

$(7xy)(3) \cdot \sqrt{(2x)(4xy^2)} = 21xy \cdot \sqrt{2 \cdot 4 \cdot x^2 \cdot y^2}$ The radical contains the squares, 4, x^2, and y^2, so take the roots of those out. $21xy \cdot 2 \cdot x \cdot y \sqrt{2}$ Then just simplify that the rest of the way.

7. CliffSedge

Also note that you could have simplified the second radical first by taking out the 2 and the y since it had 4y^2 as a perfect square already.