Question 274775
First, let's simplify {{{sqrt(486)}}}



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 486



Factors:

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486



Notice how 81 is the largest perfect square, so lets factor 486 into 81*6



{{{sqrt(81*6)}}} Factor 486 into 81*6
 
 
 
{{{sqrt(81)*sqrt(6)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
 
 
{{{9*sqrt(6)}}} Take the square root of the perfect square 81 to get 9 
 
 
 
So the expression {{{sqrt(486)}}} simplifies to {{{9*sqrt(6)}}}


In other words, {{{sqrt(486)=9*sqrt(6)}}}


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So this means that {{{4*sqrt(486)=4*9*sqrt(6)=36*sqrt(6)}}}


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Answer:


So {{{4*sqrt(486)=36*sqrt(6)}}}