How does the square root of 12 become 2 times the square root of 3?

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Answer 1 · 2015-07-06T01:20:02

#sqrt12 = 2sqrt3#

Let's factor the term inside the radical.

#sqrt12 = sqrt(2×2×3) = sqrt(2^2×3)#

We know that

#sqrt(xy) = sqrtx × sqrt y#

So

#sqrt12 = sqrt(2^2×3) = sqrt(2^2) × sqrt3#

#sqrt12 = 2 × sqrt3#

#sqrt12 = 2sqrt3#