Question

Can someone help me with Multiplying Radicals?

Answer 1

These are the problems. V

Answer 2

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

Answer 3

no @wio its confusing me.

Answer 4

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.

Answer 5

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

Answer 6

\[(7xy)(3) \cdot \sqrt{(2x)(4xy^2)} = 21xy \cdot \sqrt{2 \cdot 4 \cdot x^2 \cdot y^2}\]
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.

Answer 7

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.