SOLUTION: Simplify assume that all variables are nonnegative real numbers square root of 12

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Question 350760: Simplify assume that all variables are nonnegative real numbers
square root of 12
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2812%29 Start with the given expression



The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 12


Factors:
1, 2, 3, 4, 6, 12


Notice how 4 is the largest perfect square, so lets factor 12 into 4*3


sqrt%284%2A3%29 Factor 12 into 4*3

sqrt%284%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

2%2Asqrt%283%29 Take the square root of the perfect square 4 to get 2

So the expression sqrt%2812%29 simplifies to 2%2Asqrt%283%29

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Check:
Notice if we evaluate the square root of 12 with a calculator we get

sqrt%2812%29=3.46410161513775

and if we evaluate 2%2Asqrt%283%29 we get

2%2Asqrt%283%29=3.46410161513775

This shows that sqrt%2812%29=2%2Asqrt%283%29. So this verifies our answer


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
square root of 12
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sqrt(12)
= sqrt(4*3)
---
= sqrt(4)*sqrt(3)
---
= 2*sqrt(3)
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Cheers,
Stan H.
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