SOLUTION: Please help me add the following square roots together. sqrt12x^5 + sqrt300x^5 -2xsqrt48x^3

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Question 187924: Please help me add the following square roots together.
sqrt12x^5 + sqrt300x^5 -2xsqrt48x^3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You need to factor each of these terms and then factor out any common factor.
Let's take each term, one-by-one, and see how that's done.
sqrt%2812x%5E5%29 this can be written as:
sqrt%284%2A3%2Ax%5E4%2Ax%29 Notice that 4 and x%5E4+=+%28x%5E2%29%5E2 are perfect squares so you can take their square roots and move them outside of the radical sign.
highlight%28sqrt%2812x%5E5%29+=+2x%5E2sqrt%283x%29%29
Similarly for the second term:
sqrt%28300x%5E5%29 Factor 300 into 300+=+3%2A10%5E2 and x%5E5+=+x%2A%28x%5E2%29%5E2 and again, you have some perfect squares 10%5E2 and %28x%5E2%29%5E2 so take their square roots and move them outside of the radical sign.
highlight%28sqrt%28300x%5E5%29+=+10x%5E2%2Asqrt%283x%29%29
and for the last term:
2x%2Asqrt%2848x%5E3%29 you have 48+=+3%2A16=3%2A4%5E2 and x%5E3+=+x%2Ax%5E2, so...
2x%2Asqrt%2848x%5E3%29+=+2x%2A4x%2Asqrt%283x%29=highlight%288x%5E2sqrt%283x%29%29
Now let's put it all together:
2x%5E2%2Asqrt%283x%29%2B10x%5E2%2Asqrt%283x%29-8x%5E2%2Asqrt%283%29 Factor the common factorsqrt%283x%29 to get:
sqrt%283x%29%282x%5E2%2B10x%5E2-8x%5E2%29 Now add up the x%5E2 terms and you get:
highlight%284x%5E2%2Asqrt%283x%29%29