When you’re asked to multiply two square root expressions, what I’m going to do personally is look at the regular numbers first and the deal with the exponents second. Here is what I mean.
Look outside your square root radicands, I have 3 and 2. That tells me outside I’m going to have 6 as part of my answer. Let me write that again, my marker just didn’t work very well. Okay I’m going to have 6 as part of my outside answer. Under the square root, I have 6x times 6x which I could write as 36x². Okay if I were to break that down and do its products into the factors, write that product into its factors, I would have 6 times square root of 36 times square root of x² which is 6 times 6 times x. That’s going to be my final answer.
So I found that out by finding that 3 times 2 was that 6 that was outside the radicand all along and then I did 6x times 6x to give me 36x² and then broke that down.
The short cut way would be to remember this property, square root of a number times the square root of that same number is equal to that radicand. So if I had square root of 6x times square root of 6x and I knew that property, I could already jump down to the 6x there. However you want to do is totally fine. Sometimes it’s better to write it out so you’re making sure you’re not making any mistakes, but the final answer for that is 36x.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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