Question 350760


{{{sqrt(12)}}} 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(4*3)}}} Factor 12 into 4*3
 
{{{sqrt(4)*sqrt(3)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{2*sqrt(3)}}} Take the square root of the perfect square 4 to get 2 
 
So the expression {{{sqrt(12)}}} simplifies to {{{2*sqrt(3)}}}


----------------------------
Check:

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


{{{sqrt(12)=3.46410161513775}}}


and if we evaluate {{{2*sqrt(3)}}} we get


{{{2*sqrt(3)=3.46410161513775}}}


This shows that {{{sqrt(12)=2*sqrt(3)}}}. So this verifies our answer 



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim