SOLUTION: simplify by factoring 4√486 is

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Question 274775: simplify by factoring 4√486 is
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's simplify sqrt%28486%29


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%2881%2A6%29 Factor 486 into 81*6



sqrt%2881%29%2Asqrt%286%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



9%2Asqrt%286%29 Take the square root of the perfect square 81 to get 9



So the expression sqrt%28486%29 simplifies to 9%2Asqrt%286%29

In other words, sqrt%28486%29=9%2Asqrt%286%29

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So this means that 4%2Asqrt%28486%29=4%2A9%2Asqrt%286%29=36%2Asqrt%286%29

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Answer:

So 4%2Asqrt%28486%29=36%2Asqrt%286%29