How to Multiply Radicals | Best Math Review

This video shows multiple examples of how to multiply radicals. You can multiply and divide radicals even if they are not alike. To multiply radicals, first multiply the coefficients, then the radicands. Once you’ve done this, simplify the answer if it is possible to do so.


Multiplying Radicals
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Multiplying Radicals


You can multiply and divide radicals, even if they aren’t alike. To multiply radicals, first multiply the coefficients, and then do the same with the radicands. Finally, simplify if possible.


Let’s look at two examples. First, we have three square roots of 5 times two square roots of 11. We’re going to start by multiplying our coefficients. 3 times 2, and then we multiply our radicands. That’s the square root of 5 times 11. 3 times 2 is 6 square roots of 5 times 11 is 55. 55 is not a perfect square and it also doesn’t have any perfect square factors.


We can see because we’ve pretty much already factor treed it here, 55 is 5 times 11. Neither one of those are perfect squares either. This can’t be simplified. Therefore, 6 square roots of 55 is our answer. Let’s look at four square roots of 6 times the square root of 3. We’re going to start by multiplying our coefficients.


4 times- and the coefficient of the square root of 3 is just 1. 4 times 1 is 4. Then we have the square root of 6 times the square root of 3. We have four square roots of 6 times 3 is 18. 18 is not a perfect square, but it does have a perfect square factor. We’re going to simplify it.


4 square roots of- the perfect square factor of 18 is 9, so I’m going to rewrite it as 9 times 2, which means this is 4 times the square root of 9 times the square root of 2. We have 4 times the square root of 9. The square root of 9 is 3. This is really 4 times 3 times the square root of 2. When we multiply this all together, 4 times 3 is 12 times the square root of 2. Twelve square roots of 2.



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Last updated: 12/03/2018

 

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