How to multiply radicals

label Algebra
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everything is unclear as to simplify them and multiply them. i have a few questions that involve variables and its very confusing

May 16th, 2015

In the simplest case of multiplying radicals, here's what you do:

Multiply the numbers inside the radical.

sqrt(3) * sqrt(5) = sqrt(15).

If there are numbers outside the radical, multiply those. Those stay outside the radical. Then you multiply the numbers inside the radical. Here's an example:

2sqrt(5) * 5sqrt(7). Multiply the numbers outside: 2*5=10. This number will go in front of the new radical, which is found by multiplying the numbers inside the radical:


Those are the only two situations for multiplying radicals :)

Now, SIMPLIFYING radicals is a bit different, but all it requires is pulling out of the radical any number that has a square root (or cube root, or 4th root, whatever you happen to be working with).

So 10sqrt(48) can be simplified. It's really 10sqrt(8*6), which can be simplified further: 10sqrt(2*4*6), and 4 has a square root, so pull it out and multiply it against the outside number.

10*2 (2 being the square root of 4).

20sqrt(2*6). Are we done? Nope! Because 2*6=12, and we can simplify again.


20*2sqrt(2*3), or

40sqrt(6). Are we done? Yes! Because 6 cannot be stated as the product of any other numbers that have square roots.

Please feel free to contact me for more help :)

May 16th, 2015

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