Question 340456


{{{sqrt(432)}}} 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 432



Factors:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432



Notice how 144 is the largest perfect square, so lets factor 432 into 144*3



{{{sqrt(144*3)}}} Factor 432 into 144*3
 
 
{{{sqrt(144)*sqrt(3)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
{{{12*sqrt(3)}}} Take the square root of the perfect square 144 to get 12 
 
 
So the expression {{{sqrt(432)}}} simplifies to {{{12*sqrt(3)}}}


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Check:

Notice if we evaluate the square root of 432 with a calculator we get


{{{sqrt(432)=20.7846096908265}}}


and if we evaluate {{{12*sqrt(3)}}} we get


{{{12*sqrt(3)=20.7846096908265}}}


This shows that {{{sqrt(432)=12*sqrt(3)}}}. So this verifies our answer