Question 171503


{{{sqrt(128)}}} 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 128



Factors:

1, 2, 4, 8, 16, 32, 64, 128



Notice how 64 is the largest perfect square, so lets factor 128 into 64*2



{{{sqrt(64*2)}}} Factor 128 into 64*2
 
 
 
{{{sqrt(64)*sqrt(2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
 
{{{8*sqrt(2)}}} Take the square root of the perfect square 64 to get 8 
 
 
 
So the expression {{{sqrt(128)}}} simplifies to {{{8*sqrt(2)}}}


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Check:



Notice if we evaluate the square root of 128 with a calculator we get



{{{sqrt(128)=11.3137084989848}}}



and if we evaluate {{{8*sqrt(2)}}} we get



{{{8*sqrt(2)=11.3137084989848}}}



This shows that {{{sqrt(128)=8*sqrt(2)}}}. So this verifies our answer