How do you simplify sqrt3*sqrt3√3⋅√3?

1 Answer
charredwind
Apr 17, 2018

Multiply the radicands together and simplify.

Explanation:

Roots can be very simply combined and split by multiplying or dividing the numbers “inside” the root. I’m completely failing at explaining this concept with words, so here’s some examples.

sqrt 2 * sqrt 4 = sqrt 8√2⋅√4=√8

sqrt 8 * sqrt 2 = sqrt 16 = 4√8⋅√2=√16=4

sqrt 7 * sqrt 9 = sqrt 63√7⋅√9=√63

As you can see, sqrt a * sqrt b = sqrt (a*b)√a⋅√b=√a⋅b

So finally, to answer your question, sqrt 3 * sqrt 3 = sqrt 9 = 3√3⋅√3=√9=3

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